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Solving integrals/ cos²x*sin(x)

Integral of cos²x*sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. The integral of is when :

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                               
 |                            3   
 |    2                    cos (x)
 | cos (x)*sin(x) dx = C - -------
 |                            3   
/
$$\int \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C - \frac{\cos^{3}{\left(x \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1/3
$$\frac{1}{3}$$ 
=
= 
1/3
$$\frac{1}{3}$$ 
1/3
Numerical answer [src] 
0.333333333333333
0.333333333333333

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

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