int_0^1 x e^x , dx = . . . . . . | vedclass

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(B) To evaluate the integral $\int_0^1 x e^x \, dx$,we use the method of integration by parts: $\int u \, dv = uv - \int v \, du$. Let $u = x$ and $dv

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) To evaluate the integral $\int_0^1 x e^x \, dx$,we use the method of integration by parts: $\int u \, dv = uv - \int v \, du$. Let $u = x$ and $dv = e^x \, dx$. Then $du = dx$ and $v = e^x$. Applying the formula: $\int_0^1 x e^x \, dx = [x e^x]_0^1 - \int_0^1 e^x \, dx$ $= (1 \cdot e^1 - 0 \cdot e^0) - [e^x]_0^1$ $= (e - 0) - (e^1 - e^0)$ $= e - (e - 1)$ $= e - e + 1$ $= 1$. Thus,the correct option is $B$.

$\int_0^1 x e^x \, dx = $ . . . . . .

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