Double integral

Question

Double integral

ksaimouli · Answer

$$\int\limits_{2}^{5}\int\limits_{0}^{1}x \sqrt{4-x^2}dx dy$$

ksaimouli · Answer

@AccessDenied I used U-sub for dx and got 1

ksaimouli · Answer

@iPwnBunnies

ksaimouli · Answer

and dy I got 3

ipwnbunnies · Answer

That should be right.

ksaimouli · Answer

but the answer is 8 :-O

ipwnbunnies · Answer

Ok, hold on lol. Tryna do it in muh head. >.<

rational · Answer

rational · Answer

wolfram says $8-3\sqrt{3}$ ?

ipwnbunnies · Answer

Do the integral with respect to x again. The answer isn't 1.

ksaimouli · Answer

ur limits are incorrect

ksaimouli · Answer

my limits r incorrect lol, (2_5) and (0_2) sorry

ipwnbunnies · Answer

oh ok
hold on

rational · Answer

Alright, switching to dy dx simplifies ur work here

rational · Answer

$ \int \limits_2^5 \int \limits_0^2  x*\sqrt{4-x^2} dx dy =  \int \limits_0^2  \int \limits_2^5 x*\sqrt{4-x^2} dy dx$

ipwnbunnies · Answer

Yes, you can do that too. I would rather just get rid of the 'x' work first.

rational · Answer

nvm, it sticks in there... you will get to do the same work either way lol

ipwnbunnies · Answer

I got a different answer evaluating x anyway when the limits go from 0 to 2. I didn't get 1.

rational · Answer

ipwnbunnies · Answer

Yep.

ksaimouli · Answer

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