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Solving integrals/ sin^4(x)cos(x)

Integral of sin^4(x)cos(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                  
 --                  
 3                   
  /                  
 |                   
 |     4             
 |  sin (x)*cos(x) dx
 |                   
/                    
pi                   
--                   
6
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$ 
Integral(sin(x)^4*cos(x), (x, pi/6, pi/3))
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] 
  /                               
 |                            5   
 |    4                    sin (x)
 | sin (x)*cos(x) dx = C + -------
 |                            5   
/
$$\int \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{5}{\left(x \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            ___
   1    9*\/ 3 
- --- + -------
  160     160
$$- \frac{1}{160} + \frac{9 \sqrt{3}}{160}$$ 
=
= 
            ___
   1    9*\/ 3 
- --- + -------
  160     160
$$- \frac{1}{160} + \frac{9 \sqrt{3}}{160}$$ 
-1/160 + 9*sqrt(3)/160
Numerical answer [src] 
0.0911778579257494
0.0911778579257494

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

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