What is the integral from 0 to 1 of y/(e^{7y)} ?

The integral from 0 to 1 of y/(e^{7y)} is -8/(49e^7)+1/49

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integral from 0 to 1 of y/(e^{7y)}

\int_{0}^{1} \frac{y}{e ^{7 y}} d y

- \frac{8}{49 e ^{7}} + \frac{1}{49}

Decimal Notation

0.02025 \dots

Solution steps

\int_{0}^{1} \frac{y}{e ^{7 y}} d y

Apply Integration By Parts

: [- \frac{1}{7} e^{- 7 y} y - \int - \frac{1}{7} e^{- 7 y} d y]_{0}^{1}

= [- \frac{1}{7} e^{- 7 y} y - \int - \frac{1}{7} e^{- 7 y} d y]_{0}^{1}

\int - \frac{1}{7} e^{- 7 y} d y = \frac{1}{49} e^{- 7 y}

= [- \frac{1}{7} e^{- 7 y} y - \frac{1}{49} e^{- 7 y}]_{0}^{1}

Compute the boundaries:

- \frac{8}{49 e ^{7}} + \frac{1}{49}

= - \frac{8}{49 e ^{7}} + \frac{1}{49}

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What is the integral from 0 to 1 of y/(e^{7y)} ?
The integral from 0 to 1 of y/(e^{7y)} is -8/(49e^7)+1/49