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Volume of revolution integration for inverse sign
- Thread starter JNC
- Start date
D
Deleted member 4993
Guest
Please show us what you have tried and exactly where you are stuck.V = pi ∫ (2sin^-1(2/(y+2))+pi)^2 dy
Can't solve this for 360 degree revolution with respect to y axis... limits are from y = 0 to y = 5... is it solvable ?
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Please share your work/thoughts about this problem.
original equation is y = 2cosec(x/2+pi/2) - 2
which I have been instructed to revolve around the y-axis 360 degrees to find volume between the limits 0 and 5
When rearranged in terms of x, i got:
X = 2[sin^-1(2/(y+2))+pi/2]
= 2sin^-1(2/(y+2))+pi
To find volume it is pi ∫ x^2dy from limits 0 to 5
= pi ∫ (2sin^-1(2/(y+2))+pi)^2 dy
What I have done is expanded it and then integrated the individual parts of the integral by integration by parts... however I used substitution and put t = 2(y+2) to simplify... but it is quite difficult... not sure if it is intergratable
which I have been instructed to revolve around the y-axis 360 degrees to find volume between the limits 0 and 5
When rearranged in terms of x, i got:
X = 2[sin^-1(2/(y+2))+pi/2]
= 2sin^-1(2/(y+2))+pi
To find volume it is pi ∫ x^2dy from limits 0 to 5
= pi ∫ (2sin^-1(2/(y+2))+pi)^2 dy
What I have done is expanded it and then integrated the individual parts of the integral by integration by parts... however I used substitution and put t = 2(y+2) to simplify... but it is quite difficult... not sure if it is intergratable
D
Deleted member 4993
Guest
The problem - as posted - will not converge to a finite volume.original equation is y = 2cosec(x/2+pi/2) - 2
which I have been instructed to revolve around the y-axis 360 degrees to find volume between the limits 0 and 5
When rearranged in terms of x, i got:
X = 2[sin^-1(2/(y+2))+pi/2]
= 2sin^-1(2/(y+2))+pi
To find volume it is pi ∫ x^2dy from limits 0 to 5
= pi ∫ (2sin^-1(2/(y+2))+pi)^2 dy
What I have done is expanded it and then integrated the individual parts of the integral by integration by parts... however I used substitution and put t = 2(y+2) to simplify... but it is quite difficult... not sure if it is intergratable
Please post the EXACT problem as it was given to you.