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

The integral from 0 to t of 3/(sqrt(1-x^2)) is 3arcsin(t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to t of 3/(sqrt(1-x^2))

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

3 arcsin (t)

Solution steps

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

Take the constant out:

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

= 3 \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)

= 3 [arcsin (x)]_{0}^{t}

Compute the boundaries:

arcsin (t)

= 3 arcsin (t)

\int_{- 2}^{2} x^{2} + 4 d x

\int_{2}^{5} \frac{1}{( x - 2 ) ^{1}} d x

\int_{0}^{\frac{1}{9}} arccos (9 x) d x

\int_{0}^{2 π} 5 t 2 d t

\int_{0}^{2} \frac{2 x ^{2} - 6 x}{2} d x

What is the integral from 0 to t of 3/(sqrt(1-x^2)) ?
The integral from 0 to t of 3/(sqrt(1-x^2)) is 3arcsin(t)