Changing order of integration

**studentsteve1202** · April 27th 2008, 05:56 AM

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?

**mr fantastic** · April 27th 2008, 06:13 AM

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 ....!?

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

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