Solve the problem.
-What region in the xy-plane maximizes the value of
$$\int _ { R } \int \left( 1600 - 64 x ^ { 2 } - 25 y ^ { 2 } \right) d A ?$$
A) The ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$
B) The ellipse $25 x ^ { 2 } + 64 y ^ { 2 } = 1600$
C) The ellipse $64 x ^ { 2 } + 25 y ^ { 2 } = 1$
D) The ellipse $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The integrand is maximized when $x^2$ and $y^2$ are minimized. This occurs when the ellipse is at its smallest, which is when the major and minor axes are equal. The ellipse with equal major and minor axes is the circle, which is choice A.

Solve the Problem ∫R∫(1600−64x2−25y2)dA?\int _ { R } \int \left( 1600 - 64 x ^ { 2 } - 25 y ^ { 2 } \right) d A ?∫R​∫(1600−64x2−25y2)dA?

Solve the Problem $\int _ { R } \int \left( 1600 - 64 x ^ { 2 } - 25 y ^ { 2 } \right) d A ?$