Question

this should be really simple but i can't figure out why i'm getting the wrong answer.....

Evaluate the iterated integral ∫2,0∫1,04x^2y^3dxdy

Answer 1

you have plugged in the incorrect limits

Answer 2

that's really blurry. i'm gonna try and do another pic.

Answer 3

i can see...
anyways,
the limits for x are 0 to 1

Answer 4

\[\int\limits_{0}^{2}\int\limits_{0}^{1}x^2*y^3*dx*dy\]

Answer 5

dx dy
means first integrate w.r.t x
then y

Answer 6

oh. how do you know which limit goes with x and which goes with y? the book doesn't really explain that.

Answer 7

yeah u did it right

Answer 8

try interchanging them

Answer 9

first with dx thn with dy

Answer 10

the innermost limits goes to the variable you integrate first

and
dx dy tells you to integrate with x first

Answer 11

so basically, inside with inside and outside with outside?

Answer 12

yess

Answer 13

ok, thanks.

Answer 14

got it. 16/3.

Answer 15

good! :)