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Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as

- $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$
- $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 yx^2 dx \: dy$
- $\displaystyle \int_{y=0}^1 \int_{x=\sqrt{y}}^1 xy^2 dx \: dy$
- $\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} yx^2 dx \: dy$