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

The integral from 0 to 1 of 3/(x^2+1) is (3pi)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x

\frac{3 π}{4}

Decimal

2.35619 \dots

Solution steps

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{1} \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 3 [arctan (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= 3 \cdot \frac{π}{4}

Simplify

= \frac{3 π}{4}

\int_{2}^{8} 4 x d x

\int_{0}^{8} 6 t^{2} - 2 t + 5 d t

\int_{- 8}^{8} (x^{\frac{1}{3}}) d x

\int_{0}^{4} (x + 2)^{2} d x

\int_{0}^{t} e^{- 6 t} d t

What is the integral from 0 to 1 of 3/(x^2+1) ?
The integral from 0 to 1 of 3/(x^2+1) is (3pi)/4