Evaluate each of the following integral: `int_e^(pi//2)e^x(sinx-cos x)dx`

Explanation

Consider, `I =int_{0}^{frac{pi}{2}} e^{x}(sin x-cos x) d x `

`=int_{0}^{frac{pi}{2}} e^{x} sin x d x-int_{0}^{frac{pi}{2}} e^{pi} cos x d x `

`=[sin x cdot e^{x}]_{0}^{frac{pi}{2}}-int_{0}^{frac{pi}{2}} cos x cdot e^{x} d x-int_{0}^{frac{pi}{2}} e^{x} cos x d x `

`=(sin frac{pi}{2} cdot e^{frac{pi}{2}})-2 int_{0}^{frac{pi}{2}} e^{x} cos d x `

`=e^{frac{pi}{2}}-2 int_{0}^{frac{pi}{2}} e^{x} cos x d x-(1)`


Now we have to find out `int_{0}^{frac{pi}{2}} e^{pi} cos x d x`
...