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Math Help - Calculus Question

  1. #1
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    Calculus Question

    If 0 < k < (pi/2) and the area under the curve y = cos x from x = k to x = (pi/2) is 0.1, then k =

    A) 1.471
    B) 1.414
    C) 1.277
    D) 1.120
    E) 0.436
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  2. #2
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    Quote Originally Posted by frozenflames
    If 0 < k < (pi/2) and the area under the curve y = cos x from x = k to x = (pi/2) is 0.1, then k =

    A) 1.471
    B) 1.414
    C) 1.277
    D) 1.120
    E) 0.436
    Thus, the area is,
    \int^{\pi/2}_k\cos x=.1
    Using the fundamental theorem,
    \sin(\pi/2)-\sin k=.1
    Thus,
    1-\sin k=.1
    Thus,
    \sin k=.9
    Using the arc sine we get,
    k\approx 1.12
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