Thread: 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.

Area =

In this case , so the area is

Volume = Integrate the area function on the interval

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.

Use the identity

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

Simply use the endpoints of the interval as the limits of integration. In this case the interval you need to evaluate is

You might need to split up the integral if you're dealing with a function with absolute values, e.g. on the interval

ok thank you.

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

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

The correct answer is

Thank you, Where do I find the LaTeX tutorials ?

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

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

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