1. ## confusing integral

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

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

2. 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?