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Integral of sin^2(y) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi           
  /           
 |            
 |     2      
 |  sin (y) dy
 |            
/             
0             
$$\int\limits_{0}^{\pi} \sin^{2}{\left(y \right)}\, dy$$
Integral(sin(y)^2, (y, 0, pi))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    1. The integral of a constant times a function is the constant times the integral of the function:

      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 cosine is sine:

          So, the result is:

        Now substitute back in:

      So, the result is:

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                             
 |                              
 |    2             y   sin(2*y)
 | sin (y) dy = C + - - --------
 |                  2      4    
/                               
$$\int \sin^{2}{\left(y \right)}\, dy = C + \frac{y}{2} - \frac{\sin{\left(2 y \right)}}{4}$$
The graph
The answer [src]
pi
--
2 
$$\frac{\pi}{2}$$
=
=
pi
--
2 
$$\frac{\pi}{2}$$
pi/2
Numerical answer [src]
1.5707963267949
1.5707963267949

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