How does one calculate the area of a rectangle using a single integral? The Next CEO of Stack OverflowEvaluating an integral using the Fundamental Theorem of CalculusOptimizing the area of a rectangle with one side against a wall using the am-gm inequalityHow can I tell the difference if my integral is measuring arc length or area?Proof request for finding the area of a rectangle using an ellipse and an integral.Trouble in finding the area of the curve using IntegrationCalculate integral with help the Euler's integralsGaussian Integral using single integrationCan arc length be a straight line?Area of a Rectangle using a Double Integral in Polar CoordinatesHow fast is the area of rectangle increasing?
Why is information "lost" when it got into a black hole?
Is it correct to say moon starry nights?
Defamation due to breach of confidentiality
Small nick on power cord from an electric alarm clock, and copper wiring exposed but intact
Is there an equivalent of cd - for cp or mv
Can I board the first leg of the flight without having final country's visa?
What is the difference between "hamstring tendon" and "common hamstring tendon"?
Help understanding this unsettling image of Titan, Epimetheus, and Saturn's rings?
Why is the US ranked as #45 in Press Freedom ratings, despite its extremely permissive free speech laws?
What flight has the highest ratio of timezone difference to flight time?
Can you teleport closer to a creature you are Frightened of?
Do scriptures give a method to recognize a truly self-realized person/jivanmukta?
Why am I getting "Static method cannot be referenced from a non static context: String String.valueOf(Object)"?
Traduction de « Life is a roller coaster »
Help! I cannot understand this game’s notations!
What difference does it make using sed with/without whitespaces?
Is it ok to trim down a tube patch?
Is fine stranded wire ok for main supply line?
How to get the last not-null value in an ordered column of a huge table?
Is French Guiana a (hard) EU border?
Is a distribution that is normal, but highly skewed, considered Gaussian?
Could a dragon use its wings to swim?
Can someone explain this formula for calculating Manhattan distance?
Getting Stale Gas Out of a Gas Tank w/out Dropping the Tank
How does one calculate the area of a rectangle using a single integral?
The Next CEO of Stack OverflowEvaluating an integral using the Fundamental Theorem of CalculusOptimizing the area of a rectangle with one side against a wall using the am-gm inequalityHow can I tell the difference if my integral is measuring arc length or area?Proof request for finding the area of a rectangle using an ellipse and an integral.Trouble in finding the area of the curve using IntegrationCalculate integral with help the Euler's integralsGaussian Integral using single integrationCan arc length be a straight line?Area of a Rectangle using a Double Integral in Polar CoordinatesHow fast is the area of rectangle increasing?
$begingroup$
I tried to ask this in a different way and did not correctly explain myself.
I am ok integrating the line $y = x$ , let us say from $0$ to $2$ using calculus.
If I want to get the square I can easily multiply by two and using calculus the dimensions work. The area is a square and when we integrate we have a square.
Here is my question. If I use a straight line above the x axis my equation becomes $y$ = ( some constant) . Now I use calculus and integrate from 0 to 2 , I also get the correct answer BUT I have to imagine it is a rectangle because when you ingtegrate you have one $x$ term and it is not a square. The answers match OK it's the dimensions that bother me.
I did not do a good job explaining this on my previous question. Sorry
calculus integration
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
$endgroup$
add a comment |
$begingroup$
I tried to ask this in a different way and did not correctly explain myself.
I am ok integrating the line $y = x$ , let us say from $0$ to $2$ using calculus.
If I want to get the square I can easily multiply by two and using calculus the dimensions work. The area is a square and when we integrate we have a square.
Here is my question. If I use a straight line above the x axis my equation becomes $y$ = ( some constant) . Now I use calculus and integrate from 0 to 2 , I also get the correct answer BUT I have to imagine it is a rectangle because when you ingtegrate you have one $x$ term and it is not a square. The answers match OK it's the dimensions that bother me.
I did not do a good job explaining this on my previous question. Sorry
calculus integration
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
$endgroup$
add a comment |
$begingroup$
I tried to ask this in a different way and did not correctly explain myself.
I am ok integrating the line $y = x$ , let us say from $0$ to $2$ using calculus.
If I want to get the square I can easily multiply by two and using calculus the dimensions work. The area is a square and when we integrate we have a square.
Here is my question. If I use a straight line above the x axis my equation becomes $y$ = ( some constant) . Now I use calculus and integrate from 0 to 2 , I also get the correct answer BUT I have to imagine it is a rectangle because when you ingtegrate you have one $x$ term and it is not a square. The answers match OK it's the dimensions that bother me.
I did not do a good job explaining this on my previous question. Sorry
calculus integration
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
$endgroup$
I tried to ask this in a different way and did not correctly explain myself.
I am ok integrating the line $y = x$ , let us say from $0$ to $2$ using calculus.
If I want to get the square I can easily multiply by two and using calculus the dimensions work. The area is a square and when we integrate we have a square.
Here is my question. If I use a straight line above the x axis my equation becomes $y$ = ( some constant) . Now I use calculus and integrate from 0 to 2 , I also get the correct answer BUT I have to imagine it is a rectangle because when you ingtegrate you have one $x$ term and it is not a square. The answers match OK it's the dimensions that bother me.
I did not do a good job explaining this on my previous question. Sorry
calculus integration
calculus integration
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
edited Mar 19 at 19:48
ADITYA PRAKASH
365110
365110
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
asked Mar 19 at 16:00
SedumjoySedumjoy
661316
661316
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The dimensions do work correctly in case of a rectangle as well. Let us say the height of the rectangle is $k$ and width is $b-a$.
Recall that integration is basically summing up infinitely many small rectangles with infinitesimally small widths.
$$beginalignedtextArea &=lim_nto inftysum_i=1^nunderbracek_textheightcdotunderbraceleft(dfracb-anright)_textwidth of each infinitesimal rectangle\&=int_a^bunderbracek_textunitsunderbracemathrm dx_textunits\&=kxbiggr|_a^b=k(b-a) text sq. unitsendaligned$$
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
$endgroup$
add a comment |
$begingroup$
Consider a rectangle formed by the equation $y=K$ extending from $x=a$ to $x=b$. 
Calculate the area of a small rectangular strip formed by the coordinates $(x,0)$, $(x+dx,0)$,$(x+dx,y)$ and $(x,y)$.
The area of this rectangle will be, $ydx$. Convert the whole rectangular area into smaller rectangles of area $ydx$ and sum all of them from $x=a$ to $x=b$ using integration.
The area under the curve $y=f(x)$ bounded by the X Axis and the lines $x=a$ and $x=b$ is given by,
$$int_x=a^x=bydx=int_x=a^x=bf(x)dx=int_x=a^x=bKdx=K(b-a)$$
Hope this helps...
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
$endgroup$
add a comment |
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3154244%2fhow-does-one-calculate-the-area-of-a-rectangle-using-a-single-integral%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The dimensions do work correctly in case of a rectangle as well. Let us say the height of the rectangle is $k$ and width is $b-a$.
Recall that integration is basically summing up infinitely many small rectangles with infinitesimally small widths.
$$beginalignedtextArea &=lim_nto inftysum_i=1^nunderbracek_textheightcdotunderbraceleft(dfracb-anright)_textwidth of each infinitesimal rectangle\&=int_a^bunderbracek_textunitsunderbracemathrm dx_textunits\&=kxbiggr|_a^b=k(b-a) text sq. unitsendaligned$$
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
$endgroup$
add a comment |
$begingroup$
The dimensions do work correctly in case of a rectangle as well. Let us say the height of the rectangle is $k$ and width is $b-a$.
Recall that integration is basically summing up infinitely many small rectangles with infinitesimally small widths.
$$beginalignedtextArea &=lim_nto inftysum_i=1^nunderbracek_textheightcdotunderbraceleft(dfracb-anright)_textwidth of each infinitesimal rectangle\&=int_a^bunderbracek_textunitsunderbracemathrm dx_textunits\&=kxbiggr|_a^b=k(b-a) text sq. unitsendaligned$$
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
$endgroup$
add a comment |
$begingroup$
The dimensions do work correctly in case of a rectangle as well. Let us say the height of the rectangle is $k$ and width is $b-a$.
Recall that integration is basically summing up infinitely many small rectangles with infinitesimally small widths.
$$beginalignedtextArea &=lim_nto inftysum_i=1^nunderbracek_textheightcdotunderbraceleft(dfracb-anright)_textwidth of each infinitesimal rectangle\&=int_a^bunderbracek_textunitsunderbracemathrm dx_textunits\&=kxbiggr|_a^b=k(b-a) text sq. unitsendaligned$$
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
$endgroup$
The dimensions do work correctly in case of a rectangle as well. Let us say the height of the rectangle is $k$ and width is $b-a$.
Recall that integration is basically summing up infinitely many small rectangles with infinitesimally small widths.
$$beginalignedtextArea &=lim_nto inftysum_i=1^nunderbracek_textheightcdotunderbraceleft(dfracb-anright)_textwidth of each infinitesimal rectangle\&=int_a^bunderbracek_textunitsunderbracemathrm dx_textunits\&=kxbiggr|_a^b=k(b-a) text sq. unitsendaligned$$
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
answered Mar 19 at 16:18
Paras KhoslaParas Khosla
2,716423
2,716423
add a comment |
add a comment |
$begingroup$
Consider a rectangle formed by the equation $y=K$ extending from $x=a$ to $x=b$.
Calculate the area of a small rectangular strip formed by the coordinates $(x,0)$, $(x+dx,0)$,$(x+dx,y)$ and $(x,y)$.
The area of this rectangle will be, $ydx$. Convert the whole rectangular area into smaller rectangles of area $ydx$ and sum all of them from $x=a$ to $x=b$ using integration.
The area under the curve $y=f(x)$ bounded by the X Axis and the lines $x=a$ and $x=b$ is given by,
$$int_x=a^x=bydx=int_x=a^x=bf(x)dx=int_x=a^x=bKdx=K(b-a)$$
Hope this helps...
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
$endgroup$
add a comment |
$begingroup$
Consider a rectangle formed by the equation $y=K$ extending from $x=a$ to $x=b$.
Calculate the area of a small rectangular strip formed by the coordinates $(x,0)$, $(x+dx,0)$,$(x+dx,y)$ and $(x,y)$.
The area of this rectangle will be, $ydx$. Convert the whole rectangular area into smaller rectangles of area $ydx$ and sum all of them from $x=a$ to $x=b$ using integration.
The area under the curve $y=f(x)$ bounded by the X Axis and the lines $x=a$ and $x=b$ is given by,
$$int_x=a^x=bydx=int_x=a^x=bf(x)dx=int_x=a^x=bKdx=K(b-a)$$
Hope this helps...
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
$endgroup$
add a comment |
$begingroup$
Consider a rectangle formed by the equation $y=K$ extending from $x=a$ to $x=b$.
Calculate the area of a small rectangular strip formed by the coordinates $(x,0)$, $(x+dx,0)$,$(x+dx,y)$ and $(x,y)$.
The area of this rectangle will be, $ydx$. Convert the whole rectangular area into smaller rectangles of area $ydx$ and sum all of them from $x=a$ to $x=b$ using integration.
The area under the curve $y=f(x)$ bounded by the X Axis and the lines $x=a$ and $x=b$ is given by,
$$int_x=a^x=bydx=int_x=a^x=bf(x)dx=int_x=a^x=bKdx=K(b-a)$$
Hope this helps...
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
$endgroup$
Consider a rectangle formed by the equation $y=K$ extending from $x=a$ to $x=b$.
Calculate the area of a small rectangular strip formed by the coordinates $(x,0)$, $(x+dx,0)$,$(x+dx,y)$ and $(x,y)$.
The area of this rectangle will be, $ydx$. Convert the whole rectangular area into smaller rectangles of area $ydx$ and sum all of them from $x=a$ to $x=b$ using integration.
The area under the curve $y=f(x)$ bounded by the X Axis and the lines $x=a$ and $x=b$ is given by,
$$int_x=a^x=bydx=int_x=a^x=bf(x)dx=int_x=a^x=bKdx=K(b-a)$$
Hope this helps...
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
answered Mar 19 at 17:34
SNEHIL SANYALSNEHIL SANYAL
656110
656110
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3154244%2fhow-does-one-calculate-the-area-of-a-rectangle-using-a-single-integral%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
