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Solving integrals/ sin(w*t)^2

Integral of sin(w*t)^2 dx

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The solution

You have entered [src] 
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∫01sin⁡2(tw) dw\int\limits_{0}^{1} \sin^{2}{\left(t w \right)}\, dw 
Integral(sin(w*t)^2, (w, 0, 1))
The answer (Indefinite) [src] 
                          /    w       for t = 0
                          |                     
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∫sin⁡2(tw) dw=C+w2−{wfor t=0sin⁡(2tw)2totherwise2\int \sin^{2}{\left(t w \right)}\, dw = C + \frac{w}{2} - \frac{\begin{cases} w & \text{for}\: t = 0 \\\frac{\sin{\left(2 t w \right)}}{2 t} & \text{otherwise} \end{cases}}{2}
Simplify
The answer [src] 
/t   cos(t)*sin(t)                                  
|- - -------------                                  
|2         2                                        
<-----------------  for And(t > -oo, t < oo, t != 0)
|        t                                          
|                                                   
\        0                     otherwise
{t2−sin⁡(t)cos⁡(t)2tfor t>−∞∧t<∞∧t≠00otherwise\begin{cases} \frac{\frac{t}{2} - \frac{\sin{\left(t \right)} \cos{\left(t \right)}}{2}}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases} 
=
= 
/t   cos(t)*sin(t)                                  
|- - -------------                                  
|2         2                                        
<-----------------  for And(t > -oo, t < oo, t != 0)
|        t                                          
|                                                   
\        0                     otherwise
{t2−sin⁡(t)cos⁡(t)2tfor t>−∞∧t<∞∧t≠00otherwise\begin{cases} \frac{\frac{t}{2} - \frac{\sin{\left(t \right)} \cos{\left(t \right)}}{2}}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases} 
Piecewise(((t/2 - cos(t)*sin(t)/2)/t, (t > -oo)∧(t < oo)∧(Ne(t, 0))), (0, True))

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

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