What is the integral from 0 to 4 of ye^y ?

The integral from 0 to 4 of ye^y is 3e^4+1

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integral from 0 to 4 of ye^y

\int_{0}^{4} y e^{y} d y

3 e^{4} + 1

Decimal

164.79445 \dots

Solution steps

\int_{0}^{4} y e^{y} d y

Apply Integration By Parts

: [e^{y} y - \int e^{y} d y]_{0}^{4}

= [e^{y} y - \int e^{y} d y]_{0}^{4}

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

= [e^{y} y - e^{y}]_{0}^{4}

Compute the boundaries:

3 e^{4} + 1

= 3 e^{4} + 1

\int_{0}^{\frac{π}{2}} 2 t d t

\int_{0}^{1} 2 x^{2} + x d x

\int_{2}^{5} x^{2} 4 x^{3} + 3 d x

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

\int_{2}^{9} 2 x (x - 1)^{\frac{1}{3}} d x

What is the integral from 0 to 4 of ye^y ?
The integral from 0 to 4 of ye^y is 3e^4+1