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Math Help - How to write area as integral?

  1. #1
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    Post How to write area as integral?

    The question is:
    Find the area of the region between y=sin(x) and y=x
    for 0 ≤ x ≤ pi/2.
    It's going to be a definite integral with bounds from 0 to pi/2, right? But what is the equation and how do I get it?
    Thank you!
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by maiamorbific View Post
    The question is:
    Find the area of the region between y=sin(x) and y=x
    for 0 ≤ x ≤ pi/2.
    It's going to be a definite integral with bounds from 0 to pi/2, right? But what is the equation and how do I get it?
    Thank you!
    x is greater than \sin(x) for all x>0, so you want to find the area under y=x and subtract the area under y=\sin(x). The value you want is:

    \int_0^{\pi/2}x\,dx-\int_0^{\pi/2}\sin x\,dx

    This can be rewritten as a single integral: \int_0^{\pi/2}(x-\sin x)\,dx
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