Question

Double Integral.

Answer 1

\[\int\limits_{0}^{1}\int\limits_{0}^{\sqrt{1-x^2}} x dy dx\]

Answer 2

Convert to polar coordinates? I believe it can work here.

Answer 3

Maybe not, bleh, my multivar is slipping.

Answer 4

I think you are right.

Answer 5

Converting to polar....

Answer 6

I think another way is to rewrite the terms of integration to dx dy, instead of dy dx. That way, you'll get an x^2 term in the integral, and the square root can cancel out. But ofc, you'll have to redo the limits of integration

Answer 7

Sorry that took so long. It wouldn't let me press the 'post' button.

Answer 8

I am rusty on multivar too, but I don't think switching bounds will help here because circles are symmetrical with both y and x

Answer 9

That is true, but I just thought it would be another way to solve it, given that 'x' was the integrand

Answer 10

I may be wrong but evaluating it that way gave me zero for an answer.....which seems incorrect.

Answer 11

i got that too
you can just integrate this as is; let me make sure that give zero too

Answer 12

I didn't get 0, I got a nice rational number.

Answer 13

i got zero every way
can we see your work iPwn?

Answer 14

Sorry. (1/2)x*2sqrt(1-x^2)

Answer 15

Unfortunately, my work was putting it in a calculus caluator lol.

Answer 16

yes i got a rational number too :P

Answer 17

Don't you change the terms from dy dx to r dr d(theta), or something like that?

Answer 18

I got an answer just by integrating as is

Answer 19

Ahh

Answer 20

you can do a u-sub after the inner integral

Answer 21

Thank you both (;

Answer 22

welcome!