Question

double integration

Answer 1

\[\int\limits_{0}^{1} \int\limits_{2y}^{2} 4 Cos(x^{2}) dx dy\]

Answer 2

change it to \(dydx\)

Answer 3

\(\large \mathbb{\int\limits_{0}^{1} \int\limits_{2y}^{2} 4 \cos(x^{2}) dx dy = \int\limits_{?}^{?}\left( \int\limits_{?}^{?} 4 \cos(x^{2}) dy\right) dx }\)

Answer 4

can you integrate cos x^2 w r t y?

Answer 5

when u integrate \(\int \cos(x^2)dy = \cos(x^2) \int 1 dy = \cos(x^2) * x + c\)

Answer 6

so you take cos y as a constant juss like when you do partial differentials

Answer 7

draw ur region and set up bounds

Answer 8

yes lets first draw the region

Answer 9

Now what equations do we use for that?

Answer 10

think of it like this :
we fix "y" and see how "x" is varying

Answer 11

the outer integral is dy
so, y : 0->1