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Math Help - Calculus Help Please!

  1. #1
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    Question Calculus Help Please!

    I don't understand how to do this problem. Can someone please help me?

    Use substitution to evaluate the definite integral. The integral from 0 to pi/3 of sinxcos x dx.
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  2. #2
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    Quote Originally Posted by juicysharpie View Post
    I don't understand how to do this problem. Can someone please help me?

    Use substitution to evaluate the definite integral. The integral from 0 to pi/3 of sinxcos x dx.
    \int_0^{\frac \pi3}\sin(x) \cdot \cos(x) dx

    Let u = \sin(x)

    Then \dfrac{du}{dx} = \cos(x)~\implies~du=\cos(x) dx

    Since \sin(0)=0 and \sin\left(\frac \pi3\right)= \frac12 \sqrt{3} the integral becomes:

    \int_0^{\frac \pi3}\sin(x) \cdot \cos(x) dx~\implies~\int_0^{\frac12 \sqrt{3}}udu =\left. \frac12 u^2\right|_0^{\frac12 \sqrt{3}}
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