What is the integral from 0 to 3 of (2-x)e^x ?

The integral from 0 to 3 of (2-x)e^x is -3

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integral from 0 to 3 of (2-x)e^x

\int_{0}^{3} (2 - x) e^{x} d x

- 3

Solution steps

\int_{0}^{3} (2 - x) e^{x} d x

Apply Integration By Parts

: [e^{x} (2 - x) - \int - e^{x} d x]_{0}^{3}

= [e^{x} (2 - x) - \int - e^{x} d x]_{0}^{3}

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

= [e^{x} (2 - x) - (- e^{x})]_{0}^{3}

Simplify

[e^{x} (2 - x) - (- e^{x})]_{0}^{3} : [- e^{x} x + 3 e^{x}]_{0}^{3}

= [- e^{x} x + 3 e^{x}]_{0}^{3}

Compute the boundaries:

- 3

= - 3

\frac{8}{( s + 1 ) ^{2} ( s + 2 )}

\int \frac{1}{( x - 4 ) ( x - 1 )} d x

\int_{2}^{3} \frac{7}{3 - x} d x

\frac{d}{d x} (\frac{( x ^{2} - 3 x - 4 )}{x})

x \to 0 lim (e^{a x})

What is the integral from 0 to 3 of (2-x)e^x ?
The integral from 0 to 3 of (2-x)e^x is -3