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Find the area between y=3sinx and y=3cosx over the interval [0,pi].

  • Math - ,

    Find the indefinite integral of
    3 sin x - 3 cos x.
    It is -3 sin x - 3 cos x.
    Finally, evaluate that at x = pi and subtract the value at x = 0, the two limts of integration.
    I get (0 + 3) - (0 -3(1)) = 6

    Over part of the interval, the 3 cos x curve is higher than 3 sin x. That part of the area integral is counted as negative

  • Math - ,

    As drwls noted, the cosine curve is above the sine curve from x =0 to x=pi/4 and from pi/4 to pi, the sine curve is higher.

    So the calculation has to be done in two parts

    Area = integral(3cosx - 3sinx)dx from 0 to pi/4 + integral(3sinx - 3cosx)dx from pi/4 to pi.

    I got 6√2 as a final answer

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