Question

how to solve this:

Answer 1

\[\int\limits_{0}^{4}\int\limits_{0}^{y} \sqrt{9+y^2} dxdy\]

Answer 2

do i have to use trig substitution? if so, how?

Answer 3

So..you solve for x first, what do ya get?

Answer 4

i don't even know how to start, i find it hard to integrate the equation.

Answer 5

i'm thinking of substituting 3tan(theta) to y and then i got sec^3 theta, so i need to integrate this by parts. but it became so complicated.

Answer 6

okay, you start integrating for x, so all your "y" expressions are constants and you have
\[\int\limits_{0}^{4}\int\limits_{0}^{y}\sqrt{9+y^2}dxdy=\int\limits_{0}^{4}\sqrt{9+y^2}*x|(0toy)dy\]
\[\int\limits_{0}^{4}\sqrt{9+y^2}(y-0)dy=\int\limits_{0}^{4}y\sqrt{9+y^2}dy\]

Answer 7

oh yes i forgot, y must be constant first! thanks!!!

Answer 8

i mean i must treat y as a constant*