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Thread: Please help with a problem about definite integrals?

  1. #1
    Junior Member
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    Please help with a problem about definite integrals?

    Hi everyone. I'm going through a problem on definite integrals at the moment (attached picture). I went online to try and find some sort of guide for the solution and managed to find something close enough. It is on this link: https://www.quora.com/How-do-you-sol...sqrt-16-x-2-dx

    When I first tried to solve the problem, I did the usual method of substituting u and du. That didn't seem to work... In the link above, I see that they substituted x with 4sint instead. Why is that the case? Can someone please explain to me the reason behind this?

    Thank you very much for your responses!
    Attached Thumbnails Attached Thumbnails Please help with a problem about definite integrals?-document-7_2.jpg  
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  2. #2
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    Re: Please help with a problem about definite integrals?

    Yes, this can be done using a trigonometric substitution. But maybe you haven't learnt that way yet.

    I think this problem might be trying to get you to visualise the problem. Draw a graph and interpret the definite integral as the area under the curve.

    The graph of $\displaystyle y = \sqrt{16-x^2}$ is the top half of the circle with radius 4 and centre the origin. What is the area under the curve from x=-4 to x=4 (without using calculus)?
    Thanks from topsquark
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