Question

∫∫ x sqrt(y^2-x^2) dA, R={(x,y)|0≤x≤y, 1≤x≤2}

Answer 1

This:
\[\LARGE \int\limits(\int\limits~x~\sqrt{y^2-x^2})dA\]

Answer 2

Wait, are those the limits on the right?

Answer 3

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

Answer 4

yes

Answer 5

ok thanks

Answer 6

luigi do you know fubini's theorem?

Answer 7

the answer is \[5(2\sqrt{2}-1)/4\]

Answer 8

Knew it.

Answer 9

please show me the solution

Answer 10

oh I thought luigi asked this... mb

Answer 11

wait no.. I'm sorry I was kidding.. ;-;

Answer 12

lol

Answer 13

R={(x,y)|0≤x≤y, 1≤x≤2}
Integrate with respect to y first.

Answer 14

what type is it? type one or type two?
type one is dydx with this drawing of a vertical line and the limits are on the horizontal x axis
type two is dxdy with a drawing of a horizontal line and the limits are on the veritical y axis

Answer 15

well we can tell according to the limits...if it's all numbers it's usually at the outer integral so in this case we have a dxdy so type 2

Answer 16

because if we integrate with respect to y first we have a problem...you shouldn't have any variables

Answer 17

if we switch the problem around we need the new limits of integration... sadly my calculus iv professor umm sucks hardcore...