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  1. #1
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    definate integrals.--please help.

    please could someone solve the following definate integrals. help will be much appreciated.

    A)
    <br />
\int_0^{\pi^2} \left(\sin 4\theta - \cos 4\theta\right)^2d\theta<br />

    Note: the pi is supposed to be pi over 2 rather than squared.

    B)
    <br />
\int_1^2(15x^3+e^2x-\frac{4}{x})dx<br />
    Last edited by Diane Charlton; March 9th 2008 at 05:20 AM. Reason: definate integrals.--please help.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Diane Charlton View Post
    <br />
\int_0^{\pi^2} \left(\sin 4\theta - \cos 4\theta\right)^2d\theta<br />

    Note: the pi is supposed to be pi over 2 rather than squared.
    Then you mean
    \int_0^{\pi/2} ( sin(4 \theta) - cos(4 \theta))^2~d\theta

    = \int_0^{\pi/2} ( sin^2(4 \theta) - 2sin(4 \theta)~cos(4 \theta) + cos^2(4 \theta) )~d\theta

    = \int_0^{\pi/2} ( 1 - 2sin(4 \theta)~cos(4 \theta))~d\theta

    = \int_0^{\pi/2} ( 1 - sin(8 \theta))~d\theta

    Which I'm sure you can do easily now.

    -Dan
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