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Math Help - I don't like Integrals. Help PLEASE

  1. #1
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    I don't like Integrals. Help PLEASE

    Hi again, guys. Tomorrow I will be getting some tutoring help with Integrals so I'm hoping you guys help me out with 2 integral questions. Please and thank you! <3

    Here are the problems:

    \int 8csc(8x-9)dx

    and

    \int^{\frac{2\pi}{3}}_0 tan(\frac{x}{2})dx

    Help me, please.
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  2. #2
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    Quote Originally Posted by RedSpades View Post
    Hi again, guys. Tomorrow I will be getting some tutoring help with Integrals so I'm hoping you guys help me out with 2 integral questions. Please and thank you! <3

    Here are the problems:

    \int 8csc(8x-9)dx

    and

    \int^{\frac{2\pi}{3}}_0 tan(\frac{x}{2})dx

    Help me, please.
    For the first one, try u = 8x-9...You end up with csc(u). Simply by multiplying \frac{\csc{u}+\cot{u}}{\csc{u}+\cot{u}} with \csc{u} you get an integral of the form:
    \int \frac{f'(x)}{f(x)}~dx

    You see that this is a ln antiderivative form right away.

    As for the second one, simply multiply by \frac{\sec{\frac{x}{2}}}{\sec{\frac{x}{2}}}...Against, this is a ln antiderivative.
    Last edited by Chop Suey; October 15th 2008 at 08:48 AM.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chop Suey View Post
    As for the second one, simply multiply by \frac{\sec{\frac{x}{2}}}{\sec{\frac{x}{2}}}...Against, this is a ln antiderivative.
    You can make it a tad easier by applying the definition of tangent...because I would not have thought to multiply through by \frac{\sec\left(\frac{x}{2}\right)}{\sec\left(\fra  c{x}{2}\right)} [you'll end up with the same thing anyway]

    \tan\left(\frac{x}{2}\right)=\frac{\sin\left(\disp  laystyle\frac{x}{2}\right)}{\cos\left(\displaystyl  e\frac{x}{2}\right)}

    Then the u-substitution becomes obvious....

    --Chris
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    You can make it a tad easier by applying the definition of tangent
    I know, but I just thought I'd do things differently every once in a while.
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