What is the integral from 0 to 3 of pi(1/(x+6))^2 ?

The integral from 0 to 3 of pi(1/(x+6))^2 is pi/(18)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of pi(1/(x+6))^2

\int_{0}^{3} π (\frac{1}{x + 6})^{2} d x

\frac{π}{18}

Decimal

0.17453 \dots

Solution steps

\int_{0}^{3} π (\frac{1}{x + 6})^{2} d x

Take the constant out:

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

= π \cdot \int_{0}^{3} (\frac{1}{x + 6})^{2} d x

Simplify

(\frac{1}{x + 6})^{2} : \frac{1}{( x + 6 ) ^{2}}

= π \cdot \int_{0}^{3} \frac{1}{( x + 6 ) ^{2}} d x

Apply u-substitution

: \int_{6}^{9} \frac{1}{u ^{2}} d u

= π \cdot \int_{6}^{9} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{6}^{9}

= π [- \frac{1}{u}]_{6}^{9}

Compute the boundaries:

\frac{1}{18}

= π \frac{1}{18}

Simplify

= \frac{π}{18}

\int ln (4 x + 1) d x

3 x^{2} + 12 x - 36

\frac{d}{d x} (\frac{3 x ^{4}}{( 2 - x ^{5} ) ^{3}})

\frac{d}{d x} (5 x^{2})

n = 0 \sum \infty tan (\frac{1}{n})

What is the integral from 0 to 3 of pi(1/(x+6))^2 ?
The integral from 0 to 3 of pi(1/(x+6))^2 is pi/(18)