What region R in the xy-plane maximizes the value of
(integrand given below)
Give reasons for your answer.

Question

anonymous · Answer

$$\int\limits\limits_{}^{} \int\limits\limits_{R}^{} (4-x ^{2}-2y ^{2}) dA$$

anonymous · Answer

I know I should keep the postive integrand, but I don't know how to come up to the answer.

dumbcow · Answer

hmm if you set the function equal to 0, the result is an ellipse

not sure if that works with double integrals though (maximize by differentiating and setting = to 0)

anonymous · Answer

@dumbcow How to differentiate?

dumbcow · Answer

thats what i mean the derivative of the integral is 4-x^2 -2y^2

but not sure if that applies for double integrals ?

anonymous · Answer

do you mean the answer is x^2 + y^2 <=4?