What is the integral from a to b of xe^x ?

The integral from a to b of xe^x is be^b-e^b-ae^a+e^a

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integral from a to b of xe^x

\int_{a}^{b} x e^{x} d x

b e^{b} - e^{b} - a e^{a} + e^{a}

Solution steps

\int_{a}^{b} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{a}^{b}

= [e^{x} x - \int e^{x} d x]_{a}^{b}

\int e^{x} d x = e^{x}

= [e^{x} x - e^{x}]_{a}^{b}

Compute the boundaries:

b e^{b} - e^{b} - a e^{a} + e^{a}

= b e^{b} - e^{b} - a e^{a} + e^{a}

\int_{1}^{4} \frac{( 3 x ^{2} + 2 x + 1 )}{x} d x

\int_{0}^{4} x^{3} - 10 x^{2} + 24 x d x

\int_{- 1}^{1} \frac{x ^{3} + 1}{1 + x ^{2}} d x

\int_{2}^{6} (3 + 4 x^{2}) d x

\int_{9}^{10} (x x - 9) d x

What is the integral from a to b of xe^x ?
The integral from a to b of xe^x is be^b-e^b-ae^a+e^a