Mister Exam

Other calculators

Solving integrals/ arccos(x)^3

Integral of arccos(x)^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |      3      
 |  acos (x) dx
 |             
/              
0
$$\int\limits_{0}^{1} \operatorname{acos}^{3}{\left(x \right)}\, dx$$ 
Integral(acos(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                   
 |                        ________                                   ________         
 |     3                 /      2          3                        /      2      2   
 | acos (x) dx = C + 6*\/  1 - x   + x*acos (x) - 6*x*acos(x) - 3*\/  1 - x  *acos (x)
 |                                                                                    
/
$$\int \operatorname{acos}^{3}{\left(x \right)}\, dx = C + x \operatorname{acos}^{3}{\left(x \right)} - 6 x \operatorname{acos}{\left(x \right)} - 3 \sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)} + 6 \sqrt{1 - x^{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         2
     3*pi 
-6 + -----
       4
$$-6 + \frac{3 \pi^{2}}{4}$$ 
=
= 
         2
     3*pi 
-6 + -----
       4
$$-6 + \frac{3 \pi^{2}}{4}$$ 
-6 + 3*pi^2/4
Numerical answer [src] 
1.40220330081702
1.40220330081702

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

    © Mister Exam – Calculator