# Thread: Trig volume integration

1. ## Trig volume integration

A pottery jar has circular cross sections of radius 4+sinx/2 inches for 0 greater thanor equal to x less than or equal to pi. Sketch the figure and compute the volume.

Please help me with this problem I've never done a problem like this before. Integrating a trig function for volume.

2. Area = $\pi r^2$

In this case $r = 4+\frac{\sin x}{2}$, so the area is $\pi\left(4+\frac{\sin x}{2}\right)^2$

Volume = Integrate the area function on the interval $0 \leq x \leq \pi$

3. In the question the the the 2 in the denominator is only under the x, would that make a difference ? also there is a note/hint that tell you to look up the integral for sine squared in the back of the book. There is a table of integrals. because we never learned to integrate a trig function to a power.

4. Use the identity $\sin^2 x = \frac{1-\cos 2x}{2}$

5. Thank you. One more thing how do I integrate on a given interval ?

6. Simply use the endpoints of the interval as the limits of integration. In this case the interval you need to evaluate is $\int_0^{\pi}\pi\left(4+\sin\frac{ x}{2}\right)^2 dx$

You might need to split up the integral if you're dealing with a function with absolute values, e.g. $f(x) = |x|$ on the interval $(-1, 1)$

7. ok thank you.

8. When I foil (4+sin(x/2))^2, I get sin^2(x^2/4)+ 8sin(x/2)+16. is this correct ?

9. You should check out the LaTeX tutorials so that you can make your posts more readable.

The correct answer is $\sin ^2\left({\frac{x}{2}\right)+8\sin \left({\frac{x}{2}\right) +16$

10. Thank you, Where do I find the LaTeX tutorials ?

11. http://www.mathhelpforum.com/math-help/f47/

You can also try quoting other people in order to examine the LaTeX code for their posts.

12. Ok i'll learn how to do it. thank you