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Popular Calculus >

integral of (-x)/2

Solution

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

Solution

- \frac{x ^{2}}{4} + C

Solution steps

\int \frac{- 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 d x

Simplify

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

Apply the Power Rule

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

Simplify

(- \frac{1}{2}) \frac{x ^{2}}{2} : - \frac{x ^{2}}{4}

= - \frac{x ^{2}}{4}

Add a constant to the solution

= - \frac{x ^{2}}{4} + C

Graph

Popular Examples

integral of sin(sqrt(1+2x))

\int sin (1 + 2 x) d x

integral of 3/((2x-1)^2)

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

integral of cos(24x)

\int cos (24 x) d x

integral of sqrt(x)+1/(3sqrt(x))

\int x + \frac{1}{3 x} d x

integral of (1+2x)^3

\int (1 + 2 x)^{3} d x

Frequently Asked Questions (FAQ)

What is the integral of (-x)/2 ?
The integral of (-x)/2 is -(x^2)/4+C