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Math Help - integrals by substitution

  1. #1
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    integrals by substitution

    \int (1/ \sqrt{x})\  sin\sqrt{x}\ dx\    <br />
u=\sqrt{x}\

    the answer is -2cos(\sqrt{x})+C but cant seem to get there
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by vinson24 View Post
    \int (1/ \sqrt{x})\  sin\sqrt{x}\ dx\    <br />
u=\sqrt{x}\

    the answer is -2cos(\sqrt{x})+C but cant seem to get there
    Since they let u=\sqrt{x}, this implies that \,du=\frac{\,dx}{2\sqrt{x}}

    Now, we see that \int\frac{1}{\sqrt{x}}\sin\sqrt{x}\,dx\implies 2\int\frac{1}{2\sqrt{x}}\sin\sqrt{x}\,dx\implies 2\int\sin u\,du

    Can you take it from here?

    --Chris
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  3. #3
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    let u = sqrt x
    du = dx / 2sqrt x

    substitute to the equation you will get, the following

    2 integrate sin u du

    I think you should be able to take it from here.
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  4. #4
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    thanks see it now
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  5. #5
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    You need to put 2 outside of the integration to take care of the 1/2 that is inside the equation. If you do not put the 2 outside. The original equation would have been changed. The 2 is to prevent that from happening Hope it helps.
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