Problem - 4601
Let $$f(x)=\left\{\begin{array}{ll} \cos{x} &, x\in[-\frac{\pi}{2}, 0)\\e^x&,x\in[0,1] \end{array}\right.$$
Compute $\displaystyle\int_{-\frac{\pi}{2}}^{1}f(x)dx$.
$$\int_{-\frac{\pi}{2}}^{1}f(x)d{x} = \int_{-\frac{\pi}{2}}^{0}f(x)d{x} + \int_{0}^{1}f(x)d{x}=\left.\sin{x}\right|_{-\frac{\pi}{2}}^{0} + \left.e^x\right|_0^1 =\boxed{e}$$