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Math Help - Upper and Lower estimates of double integrals?

  1. #1
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    Upper and Lower estimates of double integrals?

    Using the maxima and minima of the function, produce upper and lower estimates of the integral I=\int\int6\cos(x-y)dA, where R is the region [0,1]x[0,1].

    ??? < I < ???

    Can someone please help me I have no idea how to do this!!

    Thanks so much
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  2. #2
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    Quote Originally Posted by mathxlover View Post
    Using the maxima and minima of the function, produce upper and lower estimates of the integral I=\int\int6\cos(x-y)dA, where R is the region [0,1]x[0,1].

    ??? < I < ???

    Can someone please help me I have no idea how to do this!!

    Thanks so much
    Here's a natural bound on the integrand: -6\leq6cos(x-y)\leq6.

    But to be more precise, you can find the extreme points on the function by setting the partial derivatives to zero: f_x = 0 and f_y = 0. Then you need to calculate the Hessian matrix to check if the points found are max, min or saddle points. Also compare these points to the boundary values.
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