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cos(x)*sin(x)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                 
  /                 
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 |  cos(x)*sin(x) dx
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$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral(cos(x)*sin(x), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    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:

    Method #2

    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]
  /                          2   
 |                        cos (x)
 | cos(x)*sin(x) dx = C - -------
 |                           2   
/                                
$$\int \sin{\left(x \right)} \cos{\left(x \right)}\, dx = C - \frac{\cos^{2}{\left(x \right)}}{2}$$
The graph
The answer [src]
   2   
sin (1)
-------
   2   
$$\frac{\sin^{2}{\left(1 \right)}}{2}$$
=
=
   2   
sin (1)
-------
   2   
$$\frac{\sin^{2}{\left(1 \right)}}{2}$$
Numerical answer [src]
0.354036709136786
0.354036709136786
The graph
Integral of cos(x)*sin(x) dx

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