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Solving integrals/ sin2wt*sin2wt

Integral of sin2wt*sin2wt dt

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2*pi                        
 ----                        
  w                          
   /                         
  |                          
  |  sin(2*w)*t*sin(2*w)*t dt
  |                          
 /                           
 0
$$\int\limits_{0}^{\frac{2 \pi}{w}} t t \sin{\left(2 w \right)} \sin{\left(2 w \right)}\, dt$$ 
Integral(((sin(2*w)*t)*sin(2*w))*t, (t, 0, 2*pi/w))
The answer (Indefinite) [src] 
  /                                3    2     
 |                                t *sin (2*w)
 | sin(2*w)*t*sin(2*w)*t dt = C + ------------
 |                                     3      
/
$$\int t t \sin{\left(2 w \right)} \sin{\left(2 w \right)}\, dt = C + \frac{t^{3} \sin^{2}{\left(2 w \right)}}{3}$$
Simplify
The answer [src] 
    3    2     
8*pi *sin (2*w)
---------------
         3     
      3*w
$$\frac{8 \pi^{3} \sin^{2}{\left(2 w \right)}}{3 w^{3}}$$ 
=
= 
    3    2     
8*pi *sin (2*w)
---------------
         3     
      3*w
$$\frac{8 \pi^{3} \sin^{2}{\left(2 w \right)}}{3 w^{3}}$$ 
8*pi^3*sin(2*w)^2/(3*w^3)

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

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