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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

Simplify

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

Apply the Power Rule

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

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

Simplify

(- \frac{1}{2}) \frac{x ^{3}}{3} : - \frac{x ^{3}}{6}

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

Add a constant to the solution

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

Graph

Popular Examples

integral from-pi to pi of x^2

\int_{- π}^{π} x^{2} d x

limit as x approaches 4 of x/(4-x)-x^3

x \to 4 lim (\frac{x}{4 - x} - x^{3})

y^{''}+8y^'+15y=cos(x)

y^{^{''}} + 8 y^{^{'}} + 15 y = cos (x)

tangent of f(x)=3xcos(x),(pi,-3pi)tangent of

f (x) = 3 x cos (x), (π, - 3 π)

(1-e^{-x}-xe^{-x})^'

(1 - e^{- x} - x e^{- x})^{^{'}}

Frequently Asked Questions (FAQ)

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