Thread: Upper and Lower estimates of double integrals?

Using the maxima and minima of the function, produce upper and lower estimates of the integral , 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

Originally Posted by mathxlover

Using the maxima and minima of the function, produce upper and lower estimates of the integral , 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: .

But to be more precise, you can find the extreme points on the function by setting the partial derivatives to zero: and . 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.