Question

Evaluate the integral $\displaystyle{\int_{0}^{1}te^{t}dt}$

1, 2 ,3 or 4?

Answer 1

\int _0^1 te^t dt\\ [ \text{By integration of uv formula}]\\ =[t\int e^t dt] _0^1-\int _0^1 (\frac{dt}{dt}.\int e^t dt) dt\\ =[te^t] _0^1-\int _0^1 e^t dt\\ =e-0-[e^t]_0^1\\ =e-e+1\\ =1