What is the integral from y to y+1 of 2y ?

The integral from y to y+1 of 2y is 2y+1

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integral from y to y+1 of 2y

\int_{y}^{y + 1} 2 y d y

2 y + 1

Solution steps

\int_{y}^{y + 1} 2 y d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{y}^{y + 1} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{y}^{y + 1}

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

Compute the boundaries:

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

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

Simplify

= 2 y + 1

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What is the integral from y to y+1 of 2y ?
The integral from y to y+1 of 2y is 2y+1