Question

Help solve this integration

Answer 1

\[\int\limits_{0}^{2} \int\limits_{x}^{2} x \sqrt{1+y^3} dydx\]

Answer 2

so, u need help with integrating
\(\sqrt{1+y^3}dy\)
or do u want to change the order of integration ?

Answer 3

just evaluate it

Answer 4

what have u tried ?

Answer 5

i just use u = 1+y^3 then differential it

Answer 6

i think change of order is necessary.

Answer 7

could you tell me a bit more plz

Answer 8

\(\int\limits_{x=0}^{x=2} \int\limits_{y=x}^{y=2} x \sqrt{1+y^3} dydx\)
to change the order of integration,
we need to find the region in which integration is performed,
so, first, can u plot the lines y=x and y=2 ??

Answer 9

yes

Answer 10

so try to plot the 4 lines,
y=x to y=2 and x=0 to x=2
u'll get a closed region, can u tell me what region u get using the drawing tool ?

Answer 11

it's a triangle

Answer 12

yes.

Answer 13

right ?

Answer 14

yes

Answer 15

then

Answer 16

can i write that region again as
\(x=0 \: to \: x=y \\ y=0\: to \:y=2\)