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Solving integrals/ sinx*cos^2xdx

Integral of sinx*cos^2xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 1/2                 
  /                  
 |                   
 |            2      
 |  sin(x)*cos (x) dx
 |                   
/                    
0
$$\int\limits_{0}^{\frac{1}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral(sin(x)*cos(x)^2, (x, 0, 1/2))
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)
 | sin(x)*cos (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] 
       3     
1   cos (1/2)
- - ---------
3       3
$$\frac{1}{3} - \frac{\cos^{3}{\left(\frac{1}{2} \right)}}{3}$$ 
=
= 
       3     
1   cos (1/2)
- - ---------
3       3
$$\frac{1}{3} - \frac{\cos^{3}{\left(\frac{1}{2} \right)}}{3}$$ 
1/3 - cos(1/2)^3/3
Numerical answer [src] 
0.108042926055098
0.108042926055098

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

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