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Popular Calculus >

integral of 1/2 y^2

Solution

\int \frac{1}{2} y^{2} d y

Solution

\frac{y ^{3}}{6} + C

Solution steps

\int \frac{1}{2} y^{2} d y

Take the constant out:

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

= \frac{1}{2} \cdot \int y^{2} d y

Apply the Power Rule

= \frac{1}{2} \cdot \frac{y ^{3}}{3}

Simplify

\frac{1}{2} \cdot \frac{y ^{3}}{3} : \frac{y ^{3}}{6}

= \frac{y ^{3}}{6}

Add a constant to the solution

= \frac{y ^{3}}{6} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 1/2 y^2 ?
The integral of 1/2 y^2 is (y^3)/6+C