What is the integral from 0 to 6 of (36)/(x^2+36) ?

The integral from 0 to 6 of (36)/(x^2+36) is (3pi)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 6 of (36)/(x^2+36)

\int_{0}^{6} \frac{36}{x ^{2} + 36} d x

\frac{3 π}{2}

Decimal

4.71238 \dots

Solution steps

\int_{0}^{6} \frac{36}{x ^{2} + 36} d x

Take the constant out:

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

= 36 \cdot \int_{0}^{6} \frac{1}{x ^{2} + 36} d x

Apply Integral Substitution

= 36 \cdot \int_{0}^{1} \frac{1}{6 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 36 \cdot \frac{1}{6} \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 36 \cdot \frac{1}{6} [arctan (u)]_{0}^{1}

Simplify

36 \cdot \frac{1}{6} [arctan (u)]_{0}^{1} : 6 [arctan (u)]_{0}^{1}

= 6 [arctan (u)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 6 \cdot \frac{π}{4}

Simplify

= \frac{3 π}{2}

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

(2, 3), (1, 3)

n = 6 \sum \infty n^{2} - 16

2 x + y = 4, y = x, y = 0

\int 7 e^{4 x + e^{4 x}} d x

What is the integral from 0 to 6 of (36)/(x^2+36) ?
The integral from 0 to 6 of (36)/(x^2+36) is (3pi)/2