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sin^22x×cosx

Integral of sin^22x×cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                   
  /                   
 |                    
 |     22             
 |  sin  (x)*cos(x) dx
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \sin^{22}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral(sin(x)^22*cos(x), (x, 0, 1))
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]
  /                                 
 |                             23   
 |    22                    sin  (x)
 | sin  (x)*cos(x) dx = C + --------
 |                             23   
/                                   
$$\int \sin^{22}{\left(x \right)} \cos{\left(x \right)}\, dx = \frac{\sin^{23}{\left(x \right)}}{23} + C$$
The graph
The answer [src]
   23   
sin  (1)
--------
   23   
$${{\sin ^{23}1}\over{23}}$$
=
=
   23   
sin  (1)
--------
   23   
$$\frac{\sin^{23}{\left(1 \right)}}{23}$$
Numerical answer [src]
0.000820677466522084
0.000820677466522084
The graph
Integral of sin^22x×cosx dx

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