# Thread: Upper and Lower estimates of double integrals?

1. ## 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 < ???

Thanks so much

2. Originally Posted by mathxlover
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 < ???

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.