5.2 Repeated interals

1.

(a) 2(b) $${\frac{e^{2}}{2} - e + \frac{1}{2}}$$(c) $${\frac{2}{27}}$$(d) $${\frac{512}{15}}$$

2.

(a) $${\int_{0}^{1}\int_{\sqrt{y}}^{y^{1/4}}f(x,y)dxdy}$$

(b) $${\int_{-1}^{0}\int_{-x}^{1}f(x,y)dydx + \int_{0}^{1}\int_{x}^{1}f(x,y)dydx}$$

(c) $${\int_{1}^{2}\int_{1}^{y}f(x,y) dx dy + \int_{2}^{4}\int_{\frac{y}{2}}^{y}f(x,y) dx dy + \int_{4}^{8}\int_{\frac{y}{2}}^{4}f(x,y) dxdy}$$

3.

(a) $${e - 1}$$(b) $${\frac{e-1}{2}}$$(c) $1 - \sin{1}$