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Math Help - Calculus Problem

  1. #1
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    Calculus Problem

    83. What is the area of the region in the first quadrant enclosed by the graphs of y = cosx, y = x,and the y-axis?



    (A) 0.127
    (B) 0.385
    (C) 0.400
    (D) 0.600
    (E) 0.947
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by frozenflames
    83. What is the area of the region in the first quadrant enclosed by the graphs of y = cosx, y = x,and the y-axis?



    (A) 0.127
    (B) 0.385
    (C) 0.400
    (D) 0.600
    (E) 0.947
    First sketch the required area, see attachment. The required area is the
    shaded region in the figure.

    Just counting squares indicates that the area is close to 0.4, but we
    will find this area by integration. This is:

    <br />
\int_0^{x_1} \cos(x)-x\ dx<br />

    where x_1 is the solution of \cos(x)=x in [0,1].
    Now using the bisection method gives that x_1\approx  0.739<br />

    So we seek:

    <br />
\int_0^{0.739} \cos(x)-x\ dx=\left[\sin(x)-x^2/2\right]_0^{0.739}=0.400<br />

    RonL
    Attached Thumbnails Attached Thumbnails Calculus Problem-gash.png  
    Last edited by CaptainBlack; March 18th 2006 at 01:35 PM.
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  3. #3
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    I dont quite understand
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by frozenflames
    I dont quite understand
    I had not finished typing the solution so look again

    RonL
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