bounds of a Really simple triple integralCylindrical triple-integral boundsEvaluate the triple integral of $x^2+y^2$ where D is a pyramidEvaluate the triple integral where D is the region inside the cylinder $x^2 + y^2 = 1$ which is bounded…?Fining the angular bounds of a triple integral functionCorrect bounds for simple triple integral in rectangular coordinates?Confused about how to set up bounds for a triple integral for a coneEvaluating triple integral over a regionTriple Integral Problem (xyz)Triple Integral Bounds of IntegrationIntegration bounds in triple integrals
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bounds of a Really simple triple integral
Cylindrical triple-integral boundsEvaluate the triple integral of $x^2+y^2$ where D is a pyramidEvaluate the triple integral where D is the region inside the cylinder $x^2 + y^2 = 1$ which is bounded…?Fining the angular bounds of a triple integral functionCorrect bounds for simple triple integral in rectangular coordinates?Confused about how to set up bounds for a triple integral for a coneEvaluating triple integral over a regionTriple Integral Problem (xyz)Triple Integral Bounds of IntegrationIntegration bounds in triple integrals
$begingroup$
Evaluate $∫∫∫_D~~y ~dV$, where $D$ is the region below the plane $z=x+1$ , above the $xy$ plane and between the cylinders $x^2+y^2=1$, and $x^2+y^2=9$
one thing i dont get is the bounds of this integral in cylinderical coordinates.
why $ 1 leq r leq 3 $ and $ 0 leq theta leq2pi$
since $ 0 leq z leq rcostheta+1$ it shouldn't be the case.
for example when $theta = pi$ and $ r = 2$ ~~=> $rcostheta+1 < 0$ !!
the bounds according to this site
https://www.varsitytutors.com/calculus_3-help/multiple-integration/triple-integrals
integration multivariable-calculus
asked 2 days ago
Mather Mather
4108
$endgroup$
add a comment |
$begingroup$
Evaluate $∫∫∫_D~~y ~dV$, where $D$ is the region below the plane $z=x+1$ , above the $xy$ plane and between the cylinders $x^2+y^2=1$, and $x^2+y^2=9$
one thing i dont get is the bounds of this integral in cylinderical coordinates.
why $ 1 leq r leq 3 $ and $ 0 leq theta leq2pi$
since $ 0 leq z leq rcostheta+1$ it shouldn't be the case.
for example when $theta = pi$ and $ r = 2$ ~~=> $rcostheta+1 < 0$ !!
the bounds according to this site
https://www.varsitytutors.com/calculus_3-help/multiple-integration/triple-integrals
integration multivariable-calculus
asked 2 days ago
Mather Mather
4108
$endgroup$
add a comment |
$begingroup$
Evaluate $∫∫∫_D~~y ~dV$, where $D$ is the region below the plane $z=x+1$ , above the $xy$ plane and between the cylinders $x^2+y^2=1$, and $x^2+y^2=9$
one thing i dont get is the bounds of this integral in cylinderical coordinates.
why $ 1 leq r leq 3 $ and $ 0 leq theta leq2pi$
since $ 0 leq z leq rcostheta+1$ it shouldn't be the case.
for example when $theta = pi$ and $ r = 2$ ~~=> $rcostheta+1 < 0$ !!
the bounds according to this site
https://www.varsitytutors.com/calculus_3-help/multiple-integration/triple-integrals
integration multivariable-calculus
asked 2 days ago
Mather Mather
4108
$endgroup$
Evaluate $∫∫∫_D~~y ~dV$, where $D$ is the region below the plane $z=x+1$ , above the $xy$ plane and between the cylinders $x^2+y^2=1$, and $x^2+y^2=9$
one thing i dont get is the bounds of this integral in cylinderical coordinates.
why $ 1 leq r leq 3 $ and $ 0 leq theta leq2pi$
since $ 0 leq z leq rcostheta+1$ it shouldn't be the case.
for example when $theta = pi$ and $ r = 2$ ~~=> $rcostheta+1 < 0$ !!
the bounds according to this site
https://www.varsitytutors.com/calculus_3-help/multiple-integration/triple-integrals
integration multivariable-calculus
integration multivariable-calculus
asked 2 days ago
Mather Mather
4108
asked 2 days ago
Mather Mather
4108
asked 2 days ago
Mather Mather
4108
asked 2 days ago
Mather Mather
4108
asked 2 days ago
Mather Mather
4108
4108
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The solution on Varsity Tutors is wrong. (What did you expect with an online tutoring outfit?) Since the problem says the region is above the $xy$-plane, the limits for $theta$ can't be $0$ to $2pi$. This problem is do-able, but it's very messy. Use symmetry to do twice the integral $0 leq theta leq pi$. But this needs to be split into $0leq theta arctan leq pi -arctan 1/3$ and $pi=arctan 1/3 leq theta leq pi.$
The limits for $r$ in the second integral are from $1$ to the line where $z=x+1$ intersects the plane.
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
$endgroup$
add a comment |
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$begingroup$
The solution on Varsity Tutors is wrong. (What did you expect with an online tutoring outfit?) Since the problem says the region is above the $xy$-plane, the limits for $theta$ can't be $0$ to $2pi$. This problem is do-able, but it's very messy. Use symmetry to do twice the integral $0 leq theta leq pi$. But this needs to be split into $0leq theta arctan leq pi -arctan 1/3$ and $pi=arctan 1/3 leq theta leq pi.$
The limits for $r$ in the second integral are from $1$ to the line where $z=x+1$ intersects the plane.
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
$endgroup$
add a comment |
$begingroup$
The solution on Varsity Tutors is wrong. (What did you expect with an online tutoring outfit?) Since the problem says the region is above the $xy$-plane, the limits for $theta$ can't be $0$ to $2pi$. This problem is do-able, but it's very messy. Use symmetry to do twice the integral $0 leq theta leq pi$. But this needs to be split into $0leq theta arctan leq pi -arctan 1/3$ and $pi=arctan 1/3 leq theta leq pi.$
The limits for $r$ in the second integral are from $1$ to the line where $z=x+1$ intersects the plane.
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
$endgroup$
add a comment |
$begingroup$
The solution on Varsity Tutors is wrong. (What did you expect with an online tutoring outfit?) Since the problem says the region is above the $xy$-plane, the limits for $theta$ can't be $0$ to $2pi$. This problem is do-able, but it's very messy. Use symmetry to do twice the integral $0 leq theta leq pi$. But this needs to be split into $0leq theta arctan leq pi -arctan 1/3$ and $pi=arctan 1/3 leq theta leq pi.$
The limits for $r$ in the second integral are from $1$ to the line where $z=x+1$ intersects the plane.
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
$endgroup$
The solution on Varsity Tutors is wrong. (What did you expect with an online tutoring outfit?) Since the problem says the region is above the $xy$-plane, the limits for $theta$ can't be $0$ to $2pi$. This problem is do-able, but it's very messy. Use symmetry to do twice the integral $0 leq theta leq pi$. But this needs to be split into $0leq theta arctan leq pi -arctan 1/3$ and $pi=arctan 1/3 leq theta leq pi.$
The limits for $r$ in the second integral are from $1$ to the line where $z=x+1$ intersects the plane.
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
answered 2 days ago
B. GoddardB. Goddard
19.5k21442
19.5k21442
add a comment |
add a comment |
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