Asked by Anonymous
Have mercy!
Find the volume of the solid obtained by rotating y=3+2x-x^2, x+y=3 about the y-axis.
Find the volume of the solid obtained by rotating y=3+2x-x^2, x+y=3 about the y-axis.
Answers
Answered by
Steve
better integrate on x, since doing discs on y will need to separate the region into two pieces. So, using shells,
v = ∫[0,3] 2πrh dx
where r = x and h = (3+2x-x^2) - (3-x)
v = 2π∫[0,3] x((3+2x-x^2) - (3-x)) dx
= 2π∫[0,3] 3x^2-x^3 dx
= 2π(x^3 - x^4/4) [0,3]
= 27/2 π
v = ∫[0,3] 2πrh dx
where r = x and h = (3+2x-x^2) - (3-x)
v = 2π∫[0,3] x((3+2x-x^2) - (3-x)) dx
= 2π∫[0,3] 3x^2-x^3 dx
= 2π(x^3 - x^4/4) [0,3]
= 27/2 π
Answered by
Anonymous
Thank you!!!
Answered by
Anonymous
If you would check my last 2 questions. I am just completely stumped.
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