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Popular Calculus >

integral of 2/3 x

Solution

\int \frac{2}{3} x d x

Solution

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

Solution steps

\int \frac{2}{3} x d x

Take the constant out:

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

= \frac{2}{3} \cdot \int x d x

Apply the Power Rule

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

Simplify

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

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 2/3 x ?
The integral of 2/3 x is (x^2)/3+C