What is the integral from 1-y to e^y of y ?

The integral from 1-y to e^y of y is (e^{2y}-1+2y-y^2)/2

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integral from 1-y to e^y of y

\int_{1 - y}^{e^{y}} y d y

\frac{e ^{2 y} - 1 + 2 y - y ^{2}}{2}

Solution steps

\int_{1 - y}^{e^{y}} y d y

Apply the Power Rule

= [\frac{y ^{2}}{2}]_{1 - y}^{e^{y}}

Compute the boundaries:

\frac{1}{2} e^{2 y} - \frac{( 1 - y ) ^{2}}{2}

= \frac{1}{2} e^{2 y} - \frac{( 1 - y ) ^{2}}{2}

Simplify

= \frac{e ^{2 y} - 1 + 2 y - y ^{2}}{2}

What is the integral from 1-y to e^y of y ?
The integral from 1-y to e^y of y is (e^{2y}-1+2y-y^2)/2