Convert the integral below to polar coordinates and evaluate the integral.

Lim(0→4/√2) ∫ Lim(y→√(16−y2)) ∫ xy dxdy

Instructions:
Enter the limits of integration and evaluate the integral to find the volume.

Step-by-step explanation:

We are trying to evaluate this integral.

The first thing that we have to do is understand this region in the plane.

If you graph it looks something like the photo I join.

Now we need to describe that same region in polar coordinates.

That same region in polar coordinates would be

Now remember that when we do the polar transformation we use the following formula

Then our integral would be

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!