What is the integral from 0 to 1 of y/(e^{6y)} ?

The integral from 0 to 1 of y/(e^{6y)} is -7/(36e^6)+1/36

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integral from 0 to 1 of y/(e^{6y)}

\int_{0}^{1} \frac{y}{e ^{6 y}} d y

- \frac{7}{36 e ^{6}} + \frac{1}{36}

Decimal

0.02729 \dots

Solution steps

\int_{0}^{1} \frac{y}{e ^{6 y}} d y

Apply Integration By Parts

= [- \frac{1}{6} e^{- 6 y} y - \int - \frac{1}{6} e^{- 6 y} d y]_{0}^{1}

\int - \frac{1}{6} e^{- 6 y} d y = \frac{1}{36} e^{- 6 y}

= [- \frac{1}{6} e^{- 6 y} y - \frac{1}{36} e^{- 6 y}]_{0}^{1}

Compute the boundaries:

- \frac{7}{36 e ^{6}} + \frac{1}{36}

= - \frac{7}{36 e ^{6}} + \frac{1}{36}

What is the integral from 0 to 1 of y/(e^{6y)} ?
The integral from 0 to 1 of y/(e^{6y)} is -7/(36e^6)+1/36