Question

Find the volume of the solid generated when the region between the graphs f(x) = 2 sqrt(sinx) and y = 0 over the interval [0,pi] is revolved around the x-axis

Answer 1

http://www.wolframalpha.com/input/?i=2sqrt%28sin%28x%29%29+domain+0..pi

Answer 2

that is just a picture of the region
not the volume

Answer 3

itegrate \(\pi r^2\) (the area of the circle) from \(0\) to \(\pi\)
in your case it should not be hard because \(r=f(x)=2\sqrt{\sin(x)}\)

Answer 4

*integrate

Answer 5

the anti-derivative would be -4cosx+C

Answer 6

forget the C it is a definite integral

Answer 7

but yes, when you square and find the anti - derivative it is \(-4\cos(x)\)

Answer 8

oh don't forget the \(\pi\)

Answer 9

so is the anser 4pi?

Answer 10

because on my answer sheet they got 8pi

Answer 11

it is \(8\pi\)

Answer 12

\[-4\pi \cos(x)|^{\pi}_0\]
\[=-4\pi(\cos(\pi)-\cos(0))\]

Answer 13

\[=-4\pi(-1-1)\] etc

Answer 14

oh! i forgot to plug in 0

Answer 15

yeah you need that one too!

Answer 16

thank you! that really helped