Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(x^2+6x+11)
Integral of cos(3x^2+4)
Integral of arcsin(x)/(sqrt(1-x^2))
Integral of xsiny
Identical expressions
arcsin(x)/(sqrt(one -x^ two))
arc sinus of (x) divide by ( square root of (1 minus x squared ))
arc sinus of (x) divide by ( square root of (one minus x to the power of two))
arcsin(x)/(√(1-x^2))
arcsin(x)/(sqrt(1-x2))
arcsinx/sqrt1-x2
arcsin(x)/(sqrt(1-x²))
arcsin(x)/(sqrt(1-x to the power of 2))
arcsinx/sqrt1-x^2
arcsin(x) divide by (sqrt(1-x^2))
arcsin(x)/(sqrt(1-x^2))dx
Similar expressions
arcsin(x)/(sqrt(1+x^2))
(x+arcsin(x))/sqrt(1-x^2)
arcsinx/(sqrt(1-x^2))

Solving integrals/ arcsin(x)/(sqrt(1-x^2))

Integral of arcsin(x)/(sqrt(1-x^2)) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |    asin(x)     
 |  ----------- dx
 |     ________   
 |    /      2    
 |  \/  1 - x     
 |                
/                 
2

$$\int\limits_{2}^{1} \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{- x^{2} + 1}}\, dx$$

Simplify

Detail solution

Let $u = \operatorname{asin}{\left(x \right)}$ .

Then let $du = \frac{dx}{\sqrt{1 - x^{2}}}$ and substitute $du$ :

$\int u\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u\, du = \frac{u^{2}}{2}$
Now substitute $u$ back in:

$\frac{\operatorname{asin}^{2}{\left(x \right)}}{2}$
Add the constant of integration:

$\frac{\operatorname{asin}^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\operatorname{asin}^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                          2   
 |   asin(x)            asin (x)
 | ----------- dx = C + --------
 |    ________             2    
 |   /      2                   
 | \/  1 - x                    
 |                              
/

$${{\arcsin ^2x}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      2        2
  asin (2)   pi 
- -------- + ---
     2        8

$${{\pi^2}\over{8}}-{{\arcsin ^22}\over{2}}$$

      2        2
  asin (2)   pi 
- -------- + ---
     2        8

$$\frac{\pi^{2}}{8} - \frac{\operatorname{asin}^{2}{\left(2 \right)}}{2}$$

Simplify

Numerical answer [src]

(0.867189051136318 + 2.06867262644382j)

(0.867189051136318 + 2.06867262644382j)

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of arcsin(x)/(sqrt(1-x^2)) dx

Limits of integration:

The graph:

Piecewise:

The solution