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Integral of sin^30x*cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                   
 --                   
 2                    
  /                   
 |                    
 |     30             
 |  sin  (x)*cos(x) dx
 |                    
/                     
0                     
$$\int\limits_{0}^{\frac{\pi}{2}} \sin^{30}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral(sin(x)^30*cos(x), (x, 0, pi/2))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                             31   
 |    30                    sin  (x)
 | sin  (x)*cos(x) dx = C + --------
 |                             31   
/                                   
$$\int \sin^{30}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{31}{\left(x \right)}}{31}$$
The graph
The answer [src]
1/31
$$\frac{1}{31}$$
=
=
1/31
$$\frac{1}{31}$$
1/31
Numerical answer [src]
0.032258064516129
0.032258064516129

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