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Popular >

integral of-1/2 x

Solution

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

Solution

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

Solution steps

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

Apply the Power Rule

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

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

Simplify

- \frac{1}{2} \cdot \frac{x ^{2}}{2} : - \frac{x ^{2}}{4}

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

Add a constant to the solution

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

Popular Examples

integral of (x^3)/6

\int \frac{x ^{3}}{6} d x

derivative of y=(9000)/(x^2)derivative of

y = \frac{9000}{x ^{2}}

(\partial)/(\partial x)(4xyz+ln(2xyz))

\frac{\partial}{\partial x} (4 x yz + ln (2 x yz))

(sqrt(2x^4+1))/y y^'+1/6 y^3x^3=0

\frac{2 x ^{4} + 1}{y} y^{^{'}} + \frac{1}{6} y^{3} x^{3} = 0

y^{^{'}} - y^{2} = 36

Frequently Asked Questions (FAQ)

What is the integral of-1/2 x ?
The integral of-1/2 x is -(x^2)/4+C