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Solving integrals/ sin(x/2)sin(3x/2)dx

Integral of sin(x/2)sin(3x/2)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |     /x\    /3*x\   
 |  sin|-|*sin|---| dx
 |     \2/    \ 2 /   
 |                    
/                     
0
$$\int\limits_{0}^{1} \sin{\left(\frac{x}{2} \right)} \sin{\left(\frac{3 x}{2} \right)}\, dx$$ 
Integral(sin(x/2)*sin((3*x)/2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                          
 |                                           
 |    /x\    /3*x\          sin(x)   sin(2*x)
 | sin|-|*sin|---| dx = C + ------ - --------
 |    \2/    \ 2 /            2         4    
 |                                           
/
$$\int \sin{\left(\frac{x}{2} \right)} \sin{\left(\frac{3 x}{2} \right)}\, dx = C + \frac{\sin{\left(x \right)}}{2} - \frac{\sin{\left(2 x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  3*cos(3/2)*sin(1/2)   cos(1/2)*sin(3/2)
- ------------------- + -----------------
           4                    4
$$- \frac{3 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{4} + \frac{\sin{\left(\frac{3}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{4}$$ 
=
= 
  3*cos(3/2)*sin(1/2)   cos(1/2)*sin(3/2)
- ------------------- + -----------------
           4                    4
$$- \frac{3 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{3}{2} \right)}}{4} + \frac{\sin{\left(\frac{3}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{4}$$ 
-3*cos(3/2)*sin(1/2)/4 + cos(1/2)*sin(3/2)/4
Numerical answer [src] 
0.193411135697528
0.193411135697528

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

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