Find $\int_{0}^1xe^xdx$

2 -1 1 0

1

Using integration by parts $∫uv\,dx=u∫v\,dx-∫u'(∫v\,dx)dx$ $∫xe^x\,dx=x∫e^x\,dx-∫1.e^x\,dx$ $xe^x-e^x|_0^1$ $=(1.e^1-e^1)-(0-e^0)$ $=0-(0-1)$ $=1$