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if f'(x)=cos^2x and f(1)=0 then f(x)=

  • math -

    cos^2x = (1+cos2x)/2

    f(x) = x/2 + sin2x/4 + C
    at x=1,
    0 = 1/2 + 0 + C
    C = -1/2

    f(x) = x/2 + sin2x/4 - 1/2
    = 1/4 (2x + sin2x - 2)

  • math -- oops -

    0 = 1/2 + sin(2)/4 + C
    C = -1/4 (2 + sin2)

    adjust final answer accordingly

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