# Thread: Changing order of integration

1. ## Changing order of integration

Hello can anyone help me with chaging the order of integration? I'm not sure how to go about it.
i Have to evaluate the double integral of 2(x^2)ysin(x(y^3)) dx dy. The limits are 1 and 0. And 1 and square root of y.
But i'm not sure how to change the order of integration! i've tried drawing a diagram ut it went wrong. Can anybody help?

2. Originally Posted by studentsteve1202
Hello can anyone help me with chaging the order of integration? I'm not sure how to go about it.
i Have to evaluate the double integral of 2(x^2)ysin(x(y^3)) dx dy. The limits are 1 and 0. And 1 and square root of y.
But i'm not sure how to change the order of integration! i've tried drawing a diagram ut it went wrong. Can anybody help?
I can't see how your diagram can go wrong ....!?

$\int_{y=0}^{y=1} \int_{x = \sqrt{y}}^{x = 1} ..... dx \, dy = \int_{x=0}^{x=1} \int_{y = 0}^{y = x^2} ..... dy \, dx$