Integrating e^(6x^2+y^2) Over a Circular Disk with Maxima and Minima Estimation

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Homework Statement



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

int(int) e^(6(x^2+y^2))dA x^2+y^2<= 4 where D is a circlular disk

Homework Equations





The Attempt at a Solution


can someone send me off in the right direction? Like how would i use maxmia and mina of the function??
 
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Try converting to polar co-ordinates, x=r\cos\theta ,y=r\sin\theta. This should allow you to compute the integral explicitly.

Mat
 
In polar coordinates, the integrand is just e^{6r^2} which has maximum value on the boundary of the circle, where r= \sqrt{x^2+ y^2}= 2 of e^{24} and minimum at the center, where r= 0, of e^0= 1. That allows you to answer the question of "upper and lower estimates" by just multiplying the max and min by the area of the disk.
 
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