What is the integral from-1 to 1 of 1/(sqrt(4-x^2)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 1 of 1/(sqrt(4-x^2))

\int_{- 1}^{1} \frac{1}{4 - x ^{2}} d x

\frac{π}{3}

Decimal

1.04719 \dots

Solution steps

\int_{- 1}^{1} \frac{1}{4 - x ^{2}} d x

Apply Trigonometric Substitution

= \int_{- \frac{π}{6}}^{\frac{π}{6}} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{- \frac{π}{6}}^{\frac{π}{6}}

Simplify

= [u]_{- \frac{π}{6}}^{\frac{π}{6}}

Compute the boundaries:

\frac{π}{3}

= \frac{π}{3}

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