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5.2 Repeated integrals

1.

(a) $\displaystyle{0}$ (b) $\displaystyle{\frac{7}{6}}$ (c) $\displaystyle{\frac{11}{40}}$ (d) $\displaystyle{2}$ (e) $\displaystyle{\frac{1}{12}}$

2.

(a) $\displaystyle{\int_{0}^{1}\int_{y}^{\sqrt{y}}f(x,y)dx dy}$ (b) $\displaystyle{\int_{0}^{1}\int_{\sqrt{x}}^{1}f(x,y)dy dx}$

(c) $\displaystyle{\int_{0}^{1}\int_{0}^{2y}f(x,y)dx dy + \int_{1}^{3}\int_{0}^{3-y}f(x,y)dx dy}$

3.

(a) $\displaystyle{\frac{1}{3}}$ (b) $\displaystyle{\frac{5}{2}}$ (c) $\displaystyle{\frac{\pi}{2}}$