Mister Exam

Integral of sinx² dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     2      
 |  sin (x) dx
 |            
/             
0             
$$\int\limits_{0}^{1} \sin^{2}{\left(x \right)}\, dx$$
Integral(sin(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(2*x)
 | sin (x) dx = C + - - --------
 |                  2      4    
/                               
$${{x-{{\sin \left(2\,x\right)}\over{2}}}\over{2}}$$
The graph
The answer [src]
1   cos(1)*sin(1)
- - -------------
2         2      
$$-{{\sin 2-2}\over{4}}$$
=
=
1   cos(1)*sin(1)
- - -------------
2         2      
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{1}{2}$$
Numerical answer [src]
0.27267564329358
0.27267564329358
The graph
Integral of sinx² dx

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