\text { (a) (5 points) Use the midpoint rule to estimate the value of } \iint_{D} f(x, y) d A \text { where } f(x, y)=5^{-x y^{2}} \text {, and

} D \text { is the rectangle }[0,1] \times[0,1] \text {. Use } \Delta x=\Delta y=0.5 \text {. } (b) (5 points) Observe that f is decreasing as x increases and as y increases. Where would we compute values of f to find the largest possible estimate for this double integral? Explain why the actual value of the integral could not be larger than this estimate.