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Math Help - Comparison properties of integrals?

  1. #1
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    Comparison properties of integrals?

    All right. Here's the problem.

    Use this principle:
    If m ≤ f(x) ≤ M for a ≤ x ≤ b, then m(b-a) ≤ the integral ≤ M(b-a)

    And here's my specific problem:

    Use that property along with what you know about the function to estimate the value of

    http://online2.byu.edu/webwork2_file...55353ba131.png

    the answer should be in the form of "something" ≤ the integral ≤ "something"

    Does that make sense? Help?
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  2. #2
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    Quote Originally Posted by lauren72 View Post
    All right. Here's the problem.

    Use this principle:
    If m ≤ f(x) ≤ M for a ≤ x ≤ b, then m(b-a) ≤ the integral ≤ M(b-a)

    And here's my specific problem:

    Use that property along with what you know about the function to estimate the value of

    http://online2.byu.edu/webwork2_file...55353ba131.png

    the answer should be in the form of "something" ≤ the integral ≤ "something"

    Does that make sense? Help?
    f(x) = \cos{x}

    a = \frac{\pi}{6} , b = \frac{\pi}{4}

    b-a = \frac{\pi}{12}

    \frac{\sqrt{2}}{2} \le \cos{x} \le \frac{\sqrt{3}}{2}<br />

    \frac{\pi\sqrt{2}}{24} \le \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \cos{x} \le \frac{\pi\sqrt{3}}{24}
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