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

The integral from 1 to 2 of 2y is 3

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integral from 1 to 2 of 2y

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

3

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{3}{2}

= 2 \cdot \frac{3}{2}

Simplify

= 3

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