Question

Evaluate the double integral:

Answer 1

am I on the right track?

Answer 2

yup, then?

Answer 3

next step would be to isolate the inner integral \[\int\limits_{-1}^{1}\sqrt{y-x^{2}}dx\] and evaluate it, then proceed to the next intergral with respect to y

Answer 4

where is your absolute value?

Answer 5

oops, i missed that part, I just wanted to know if I was heading in the right direction at least for now :P

Answer 6

Since your y limit is (0,2) , you need break it into 2 limits (0,1) and (1,2)

Answer 7

hence the integral becomes
\(\int_0^1 \int_{-1}^1 \sqrt {| y -x^2|}dxdy +\int_1^2\int_{-1}^1 \sqrt {| y-x^2|}dxdy\)

Answer 8

why ?
because \(|y-x^2|= y -x^2 ~~if~~y -x^2 \geq 0 \iff y\geq x^2\)

Answer 9

so, when \(y\in (1,2) , y\geq x^2\) because \(x\in (-1,1)\)

Answer 10

\(|y-x^2|= -y+x^2 ~~if~~y-x^2<0 \iff y<x^2\) for this case, \(y\in(0,1)\)

Answer 11

that is why you need break the limit of y into 2 parts to apply different functions.

Answer 12

whoah that became so much more complex

Answer 13

Try this way, I will be back in 30 minutes. Need eating

Answer 14

yeah!! this problem is not easy, but doable.

Answer 15

yeah np i'll be working on it

Answer 16

this is what I get

Answer 17

3,10,17,24, ...
what will be the 100th number in the pattern?

Answer 18

3,10,17,24, ...
what will be the 100th number in the pattern?

Answer 19

3,10,17,24, ...
what will be the 100th number in the pattern?