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Math Help - Finding area under graph by integration

  1. #1
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    Unhappy Finding area under graph by integration

    Find the exact value of the area of the region enclosed between the x−axis and the
    graph of the function f(x) = 2 sin x + 2√3 cos x on the interval [0,π].
    HINT: It might be helpful to first write f in the form f(x) = Asin(x+K) for appropriate
    constants A and K.

    K=phase
    A=amplitude
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  2. #2
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    f(x)=4\sin \left( x+\frac{\pi }{3} \right), so the expected area is given by \int_{0}^{\frac{2}{3}\pi }{4\sin \left( x+\frac{\pi }{3} \right)\,dx}-\int_{\frac{2}{3}\pi }^{\pi }{4\sin \left( x+\frac{\pi }{3} \right)}\,dx.
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