Mister Exam

Other calculators

Solving integrals/ sin(x)*cos^2x

Integral of sin(x)*cos^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  pi                  
  --                  
  2                   
   /                  
  |                   
  |            2      
  |  sin(x)*cos (x) dx
  |                   
 /                    
-pi                   
----                  
 3
$$\int\limits_{- \frac{\pi}{3}}^{\frac{\pi}{2}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral(sin(x)*cos(x)^2, (x, -pi/3, 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)
 | 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] 
1/24
$$\frac{1}{24}$$ 
=
= 
1/24
$$\frac{1}{24}$$ 
1/24
Numerical answer [src] 
0.0416666666666666
0.0416666666666666

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

    © Mister Exam – Calculator