Mister Exam

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |  sin(y)*cos(y) dy
 |                  
/                   
0                   
$$\int\limits_{0}^{1} \sin{\left(y \right)} \cos{\left(y \right)}\, dy$$
Integral(sin(y)*cos(y), (y, 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 is when :

      Now substitute back in:

    Method #2

    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]
  /                          2   
 |                        sin (y)
 | sin(y)*cos(y) dy = C + -------
 |                           2   
/                                
$$-{{\cos ^2y}\over{2}}$$
The graph
The answer [src]
   2   
sin (1)
-------
   2   
$${{1}\over{2}}-{{\cos ^21}\over{2}}$$
=
=
   2   
sin (1)
-------
   2   
$$\frac{\sin^{2}{\left(1 \right)}}{2}$$
Numerical answer [src]
0.354036709136786
0.354036709136786
The graph
Integral of sin(y)*cos(y) dx

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