What is the integral of sqrt(50-x/2) ?

The integral of sqrt(50-x/2) is -4/3 (1/2 (100-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 sqrt(50-x/2)

\int 50 - \frac{x}{2} d x

- \frac{4}{3} (\frac{1}{2} (100 - x))^{\frac{3}{2}} + C

Solution steps

\int 50 - \frac{x}{2} d x

Apply u-substitution

: \int - 2 u d u

= \int - 2 u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int u d u

Apply the Power Rule

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

= - 2 \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 50 - \frac{x}{2}

= - 2 \cdot \frac{2}{3} (50 - \frac{x}{2})^{\frac{3}{2}}

Simplify

- 2 \cdot \frac{2}{3} (50 - \frac{x}{2})^{\frac{3}{2}} : - \frac{4}{3} (\frac{1}{2} (100 - x))^{\frac{3}{2}}

= - \frac{4}{3} (\frac{1}{2} (100 - x))^{\frac{3}{2}}

Add a constant to the solution

= - \frac{4}{3} (\frac{1}{2} (100 - x))^{\frac{3}{2}} + C

\frac{d x}{d y} = - \frac{x}{y}

\frac{d y}{d x} - e^{6 x + y} = 0

x \to 1 lim (\frac{1}{x ^{2}})

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 3

\int 10 ab c x^{2} d x

What is the integral of sqrt(50-x/2) ?
The integral of sqrt(50-x/2) is -4/3 (1/2 (100-x))^{3/2}+C