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Math Help - Trig volume integration

  1. #1
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    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.
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  2. #2
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    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
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  3. #3
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    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.
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  4. #4
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    Use the identity \sin^2 x = \frac{1-\cos 2x}{2}
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  5. #5
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    Thank you. One more thing how do I integrate on a given interval ?
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  6. #6
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    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)
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  7. #7
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    ok thank you.
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  8. #8
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    When I foil (4+sin(x/2))^2, I get sin^2(x^2/4)+ 8sin(x/2)+16. is this correct ?
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  9. #9
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    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
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  10. #10
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    Thank you, Where do I find the LaTeX tutorials ?
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  11. #11
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    http://www.mathhelpforum.com/math-help/f47/

    You can also try quoting other people in order to examine the LaTeX code for their posts.
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  12. #12
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    Ok i'll learn how to do it. thank you
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