What is the integral from-2 to 3 of [te^t] ?

The integral from-2 to 3 of [te^t] is 2e^3+3/(e^2)

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integral from-2 to 3 of [te^t]

\int_{- 2}^{3} [t e^{t}] d t

2 e^{3} + \frac{3}{e ^{2}}

Decimal

40.57707 \dots

Solution steps

\int_{- 2}^{3} t e^{t} d t

Apply Integration By Parts

= [e^{t} t - \int e^{t} d t]_{- 2}^{3}

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

= [e^{t} t - e^{t}]_{- 2}^{3}

Compute the boundaries:

2 e^{3} + \frac{3}{e ^{2}}

= 2 e^{3} + \frac{3}{e ^{2}}

What is the integral from-2 to 3 of [te^t] ?
The integral from-2 to 3 of [te^t] is 2e^3+3/(e^2)