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Popular >

integral of (x^2)/2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

integral from 0 to pi of sin^2(2x)

\int_{0}^{π} sin^{2} (2 x) d x

limit as x approaches 4 of 3-x

x \to 4 lim (3 - x)

y^{^{'}} = \frac{x ^{4}}{y}

y^'-1/2 y=2cos(x)

y^{^{'}} - \frac{1}{2} y = 2 cos (x)

limit as x approaches 1 of 4/(2x-2)

x \to 1 lim (\frac{4}{2 x - 2})

Frequently Asked Questions (FAQ)

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