What is the integral from 0 to x of 3y ?

The integral from 0 to x of 3y is (3x^2)/2

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integral from 0 to x of 3y

\int_{0}^{x} 3 y d y

\frac{3 x ^{2}}{2}

Solution steps

\int_{0}^{x} 3 y d y

Take the constant out:

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

= 3 \cdot \int_{0}^{x} y d y

Apply the Power Rule

= 3 [\frac{y ^{2}}{2}]_{0}^{x}

Compute the boundaries:

\frac{x ^{2}}{2}

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

Simplify

= \frac{3 x ^{2}}{2}

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What is the integral from 0 to x of 3y ?
The integral from 0 to x of 3y is (3x^2)/2