What is the integral from 0 to 1 of t*e^t ?

The integral from 0 to 1 of t*e^t is 1

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integral from 0 to 1 of t*e^t

\int_{0}^{1} t \cdot e^{t} d t

1

Solution steps

\int_{0}^{1} t e^{t} d t

Apply Integration By Parts

: [e^{t} t - \int e^{t} d t]_{0}^{1}

= [e^{t} t - \int e^{t} d t]_{0}^{1}

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

= [e^{t} t - e^{t}]_{0}^{1}

Compute the boundaries:

1

= 1

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\int_{0}^{\frac{π}{6}} 3 sec (θ) tan (θ) d θ

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

What is the integral from 0 to 1 of t*e^t ?
The integral from 0 to 1 of t*e^t is 1