Mister Exam

Integral of sinxcos²xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |            2      
 |  sin(x)*cos (x) dx
 |                   
/                    
0                    
$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$
Integral(sin(x)*cos(x)^2, (x, 0, 1))
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   
/                                 
$$\int \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C - \frac{\cos^{3}{\left(x \right)}}{3}$$
The graph
The answer [src]
       3   
1   cos (1)
- - -------
3      3   
$$\frac{1}{3} - \frac{\cos^{3}{\left(1 \right)}}{3}$$
=
=
       3   
1   cos (1)
- - -------
3      3   
$$\frac{1}{3} - \frac{\cos^{3}{\left(1 \right)}}{3}$$
1/3 - cos(1)^3/3
Numerical answer [src]
0.280757131583002
0.280757131583002
The graph
Integral of sinxcos²xdx dx

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