What is the integral from 0 to t of 5/(sqrt(1-x^2)) ?

The integral from 0 to t of 5/(sqrt(1-x^2)) is 5arcsin(t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to t of 5/(sqrt(1-x^2))

\int_{0}^{t} \frac{5}{1 - x ^{2}} d x

5 arcsin (t)

Solution steps

\int_{0}^{t} \frac{5}{1 - x ^{2}} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{t} \frac{1}{1 - x ^{2}} d x

Use the common integral:

\int \frac{1}{1 - x ^{2}} d x = arcsin (x)

= 5 [arcsin (x)]_{0}^{t}

Compute the boundaries:

arcsin (t)

= 5 arcsin (t)

What is the integral from 0 to t of 5/(sqrt(1-x^2)) ?
The integral from 0 to t of 5/(sqrt(1-x^2)) is 5arcsin(t)