What is the integral from 2 to 3 of (18)/(sqrt(3-x)) ?

The integral from 2 to 3 of (18)/(sqrt(3-x)) is 36

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 3 of (18)/(sqrt(3-x))

\int_{2}^{3} \frac{18}{3 - x} d x

36

Solution steps

\int_{2}^{3} \frac{18}{3 - x} d x

Take the constant out:

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

= 18 \cdot \int_{2}^{3} \frac{1}{3 - x} d x

Apply u-substitution

: \int_{1}^{0} - \frac{1}{u} d u

= 18 \cdot \int_{1}^{0} - \frac{1}{u} d u

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

= 18 (- \int_{0}^{1} - \frac{1}{u} d u)

Take the constant out:

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

= 18 (- (- \int_{0}^{1} \frac{1}{u} d u))

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{1}

= 18 (- (- [2 u^{\frac{1}{2}}]_{0}^{1}))

Simplify

18 (- (- [2 u^{\frac{1}{2}}]_{0}^{1})) : 18 [2 u]_{0}^{1}

= 18 [2 u]_{0}^{1}

Compute the boundaries:

2

= 18 \cdot 2

Simplify

= 36

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

y^{^{''''}} + 2 y^{^{''}} + y = 0

e^{7 x}

f (x) = 3 x + 2

\frac{d}{d x} (20 (e^{- x} - e^{- 2 x}))

What is the integral from 2 to 3 of (18)/(sqrt(3-x)) ?
The integral from 2 to 3 of (18)/(sqrt(3-x)) is 36