Question

1)integral ycos(x^2) dx
i dont know how to do this one can someone help me out

Answer 1

\[\int\limits ycos(x^2) dx\]

Answer 2

And what is y equal to?

Answer 3

this is part of the question on my hw sheet of double integarl \[\int\limits_{0}^{2}\int\limits_{y^2}^{4} ycos(x^2) dxdy\]

Answer 4

I'm new to double integral so I could be wrong. but I think I know how to do it.
First integral is in respect of x so you just treat y as constant for first integral.

\[\int\limits_{0}^{2} \int\limits_{y^2}^{4}y\cos(x^2)dxdy = \int\limits_{0}^{2}y \left[ \int\limits_{y^2}^{4} \cos(x^2)dx\right]dy\]

Do you know what this is?\[\int\cos(x^2)dx \]

Answer 5

nope

Answer 6

switch the order to dydx

Answer 7

\(\mathbb{\int\limits_{0}^{2}\int\limits_{y^2}^{4} ycos(x^2) dxdy = \int\limits_{0}^{4}\left(\int\limits_{0}^{\sqrt{x}} ycos(x^2) dy\right)dx}\)

Answer 8

http://www.wolframalpha.com/input/?i=%5Cint%5Climits_%7B0%7D%5E%7B2%7D%5Cint%5Climits_%7By%5E2%7D%5E%7B4%7D+ycos%28x%5E2%29+dxdy++-+++%5Cint%5Climits_%7B0%7D%5E%7B4%7D%5Cint%5Climits_%7B0%7D%5E%7B%5Csqrt%7Bx%7D%7D+ycos%28x%5E2%29+dydx

Answer 9

Yes, this is a good problem in which switching the order of integration is cha-ching. ;)

Answer 10

can some one please show me the steps i would be very greatful