confusing integral

**Tekken** · April 15th 2010, 02:40 AM

$\int^{x=1}_{x=0}\int^{y=x^{2}}_{y=\sqrt{x}} x.dx.dy$

Is this the same as

$\int^{x=1}_{x=0}x(\int^{y=\sqrt{x}}_{y=x^{2}}dy)dx$

Im a bit confused as regards how to switch the limits of integration around

**mr fantastic** · April 15th 2010, 02:44 AM

Originally Posted by Tekken

$\int^{x=1}_{x=0}\int^{y=x^{2}}_{y=\sqrt{x}} x.dx.dy$

Is this the same as

$\int^{x=1}_{x=0}x(\int^{y=\sqrt{x}}_{y=x^{2}}dy)dx$

Im a bit confused as regards how to switch the limits of integration around

No, it's simply $\int^{x=1}_{x=0}x(\int_{y=\sqrt{x}}^{y=x^{2}}dy)dx$ .

However, if you want to reverse the order of integration, my advice is to first draw a sketch of the region you're integrating over - have you done so?

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