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Popular >

integral of-1/2 x^2

Solution

\int - \frac{1}{2} x^{2} d x

Solution

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

Solution steps

\int - \frac{1}{2} x^{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

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(dy)/(dx)=(2x(y-1))/(x^2+3)

\frac{d y}{d x} = \frac{2 x ( y - 1 )}{x ^{2} + 3}

Frequently Asked Questions (FAQ)

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