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sin^2(2x)

Integral of sin^2(2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |     2        
 |  sin (2*x) dx
 |              
/               
0               
$$\int\limits_{0}^{1} \sin^{2}{\left(2 x \right)}\, dx$$
Integral(sin(2*x)^2, (x, 0, 1))
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               x   sin(4*x)
 | sin (2*x) dx = C + - - --------
 |                    2      8    
/                                 
$$\int \sin^{2}{\left(2 x \right)}\, dx = C + \frac{x}{2} - \frac{\sin{\left(4 x \right)}}{8}$$
The graph
The answer [src]
1   cos(2)*sin(2)
- - -------------
2         4      
$$- \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{4} + \frac{1}{2}$$
=
=
1   cos(2)*sin(2)
- - -------------
2         4      
$$- \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{4} + \frac{1}{2}$$
1/2 - cos(2)*sin(2)/4
Numerical answer [src]
0.594600311913491
0.594600311913491
The graph
Integral of sin^2(2x) dx

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