What is the integral from 0 to 2 of (24)/(x^2+4) ?

The integral from 0 to 2 of (24)/(x^2+4) is 3pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (24)/(x^2+4)

\int_{0}^{2} \frac{24}{x ^{2} + 4} d x

3 π

Decimal

9.42477 \dots

Solution steps

\int_{0}^{2} \frac{24}{x ^{2} + 4} d x

Take the constant out:

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

= 24 \cdot \int_{0}^{2} \frac{1}{x ^{2} + 4} d x

Apply Integral Substitution

= 24 \cdot \int_{0}^{1} \frac{1}{2 ( u ^{2} + 1 )} d u

Take the constant out:

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

= 24 \cdot \frac{1}{2} \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)

= 24 \cdot \frac{1}{2} [arctan (u)]_{0}^{1}

Simplify

24 \cdot \frac{1}{2} [arctan (u)]_{0}^{1} : 12 [arctan (u)]_{0}^{1}

= 12 [arctan (u)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 12 \cdot \frac{π}{4}

Simplify

= 3 π

\int_{0}^{\infty} 25 e^{- 5 x} d x

\int_{0}^{x} e^{x y} d y

\int_{2}^{8} (x^{3} - 2) d x

\int_{0}^{1} (6 x) d x

\int_{- 1}^{1} e^{- t} d t

What is the integral from 0 to 2 of (24)/(x^2+4) ?
The integral from 0 to 2 of (24)/(x^2+4) is 3pi