What is the integral from-45 to 0 of 1/(sqrt(4-x)) ?

The integral from-45 to 0 of 1/(sqrt(4-x)) is 10

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-45 to 0 of 1/(sqrt(4-x))

\int_{- 45}^{0} \frac{1}{4 - x} d x

10

Solution steps

\int_{- 45}^{0} \frac{1}{4 - x} d x

Apply u-substitution

: \int_{49}^{4} - \frac{1}{u} d u

= \int_{49}^{4} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{4}^{49} - \frac{1}{u} d u

Take the constant out:

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

= - (- \int_{4}^{49} \frac{1}{u} d u)

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{4}^{49}

= - (- [2 u^{\frac{1}{2}}]_{4}^{49})

Simplify

- (- [2 u^{\frac{1}{2}}]_{4}^{49}) : [2 u]_{4}^{49}

= [2 u]_{4}^{49}

Compute the boundaries:

10

= 10

n = 1 \sum \infty 8^{- n}

\frac{\partial}{\partial x} (1 + e^{- x y} cos (y))

\int 2 cos (4 x) cos (2 x) d x

\int 4 1 - x^{2} d x

(5 x - 2 x^{4})^{3}

What is the integral from-45 to 0 of 1/(sqrt(4-x)) ?
The integral from-45 to 0 of 1/(sqrt(4-x)) is 10