Question

Find double integral of 6xy+6ydA with respect to the bounds x^2+y^2=16,y=0,y=3x.

Answer 1

My work:
\[\int\limits_{0}^{4}\int\limits_{0}^{3x}6xy+6y dy dx\] = 2034

Unfortunately, it's incorrect

Answer 2

=**2304

Answer 3

did you graph the region over which we are integrating

Answer 4

lets do that first

Answer 5

one way you can do it

Answer 6

Polar? I thought the calculation wouldn't be fun. Because the function is 6xy + 6y

Answer 7

i think you can do it rectangularly

Answer 8

you have to find that intersection point `c`,
where does x^2+y^2 = 16 intersect y = 3x, that x value

Answer 9

(2/5)*sqrt(10)

Answer 10

Oh! That makes a lot of sense!
I see my problem. Thanks so much!!
Would rectangularly be the best way to solve it by the way?