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Formula for surface area with respect to x or y. Why is the radius for both y?
The Next CEO of Stack OverflowWhy can't I use the disk method to compute surface area?Integrating the formula for a circle's areaWhy do we care about the 'rapidness' for convergence?Volume by rotation: Cyndrilical shells and radiiArea below x axis not considered when finding volume of shape rotated around y axis?Integration of x^(1/2) sinxWhy is surface area not simply $2 pi int_a^b (y) dx$ instead of $2 pi int_a^b (y cdot sqrt1 + y'^2) dx$?Should the Volume of a Solid of Revolution always be the same when rotated around the x-axis than around y-axis?Volume of solid revolution 2Why does wolfram answer as such in this example for surface area and volume of revolution on an area crossing the axis?
$begingroup$
I am reading this text in the stewart text:
and I'm wondering if the text here is correct. For (6), why is it $2pi*y$ and not $2 pi x$? Isn't x rotated around the y axis since it's a function of y? I guess that's not true since just because a function is a function of y doesn't mean x is the radius right? And we use $$fracdxdy$$ in 6 because that's what the function's derivative is since the function is written as a function of y right?
integration
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
$endgroup$
add a comment |
$begingroup$
I am reading this text in the stewart text:
and I'm wondering if the text here is correct. For (6), why is it $2pi*y$ and not $2 pi x$? Isn't x rotated around the y axis since it's a function of y? I guess that's not true since just because a function is a function of y doesn't mean x is the radius right? And we use $$fracdxdy$$ in 6 because that's what the function's derivative is since the function is written as a function of y right?
integration
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
$endgroup$
add a comment |
$begingroup$
I am reading this text in the stewart text:
and I'm wondering if the text here is correct. For (6), why is it $2pi*y$ and not $2 pi x$? Isn't x rotated around the y axis since it's a function of y? I guess that's not true since just because a function is a function of y doesn't mean x is the radius right? And we use $$fracdxdy$$ in 6 because that's what the function's derivative is since the function is written as a function of y right?
integration
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
$endgroup$
I am reading this text in the stewart text:
and I'm wondering if the text here is correct. For (6), why is it $2pi*y$ and not $2 pi x$? Isn't x rotated around the y axis since it's a function of y? I guess that's not true since just because a function is a function of y doesn't mean x is the radius right? And we use $$fracdxdy$$ in 6 because that's what the function's derivative is since the function is written as a function of y right?
integration
integration
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
asked Mar 18 at 20:17
Jwan622Jwan622
2,32211632
2,32211632
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Yes, the text shown has a typo in equation 6; it should read $2pi x$ rather than $2pi y$.
edited Mar 18 at 21:17
Robert Howard
2,2783935
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
$endgroup$
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
add a comment |
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes, the text shown has a typo in equation 6; it should read $2pi x$ rather than $2pi y$.
edited Mar 18 at 21:17
Robert Howard
2,2783935
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
$endgroup$
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
add a comment |
$begingroup$
Yes, the text shown has a typo in equation 6; it should read $2pi x$ rather than $2pi y$.
edited Mar 18 at 21:17
Robert Howard
2,2783935
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
$endgroup$
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
add a comment |
$begingroup$
Yes, the text shown has a typo in equation 6; it should read $2pi x$ rather than $2pi y$.
edited Mar 18 at 21:17
Robert Howard
2,2783935
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
$endgroup$
Yes, the text shown has a typo in equation 6; it should read $2pi x$ rather than $2pi y$.
edited Mar 18 at 21:17
Robert Howard
2,2783935
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
edited Mar 18 at 21:17
Robert Howard
2,2783935
edited Mar 18 at 21:17
Robert Howard
2,2783935
edited Mar 18 at 21:17
Robert Howard
2,2783935
2,2783935
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
answered Mar 18 at 20:29
Mark FischlerMark Fischler
33.8k12552
33.8k12552
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
add a comment |
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
do others agree??? Or am I wrong for thinking this?
$endgroup$
– Jwan622
Mar 18 at 20:34
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
$begingroup$
I think I misunderstood something about what limits of integration to use... if the arc length formula that I use uses dy, then the limits of integration have to be for y. Conversely, if the arc length formula I use uses dx, then the limits have to be for x right?
$endgroup$
– Jwan622
Mar 22 at 19:00
add a comment |
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