What is the integral of-1/2 x^{1/2} ?

The integral of-1/2 x^{1/2} is -1/3 x^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1/2 x^{1/2}

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

- \frac{1}{3} x^{\frac{3}{2}} + C

Solution steps

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

Apply the Power Rule

: \frac{2}{3} x^{\frac{3}{2}}

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

Simplify

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

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

Add a constant to the solution

= - \frac{1}{3} x^{\frac{3}{2}} + C

f (x) = - 3 x^{2} + 3 x + 1, at x = 1

y = \frac{2}{1 - 9 x ^{2}}

\int_{0}^{\frac{π}{2}} x cos (\frac{x}{3}) d x

\frac{2 ln ( x )}{x}

\frac{d y}{d x} = 2 y (9 - y)

What is the integral of-1/2 x^{1/2} ?
The integral of-1/2 x^{1/2} is -1/3 x^{3/2}+C