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Solving integrals/ sin(w*t)

Integral of sin(w*t) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  sin(w*t) dw
 |             
/              
0
$$\int\limits_{0}^{1} \sin{\left(t w \right)}\, dw$$ 
Integral(sin(w*t), (w, 0, 1))
The answer (Indefinite) [src] 
  /                  //-cos(w*t)             \
 |                   ||----------  for t != 0|
 | sin(w*t) dw = C + |<    t                 |
 |                   ||                      |
/                    \\    0       otherwise /
$$\int \sin{\left(t w \right)}\, dw = C + \begin{cases} - \frac{\cos{\left(t w \right)}}{t} & \text{for}\: t \neq 0 \\0 & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/1   cos(t)                                  
|- - ------  for And(t > -oo, t < oo, t != 0)
$$\begin{cases} - \frac{\cos{\left(t \right)}}{t} + \frac{1}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases}$$ 
=
= 
/1   cos(t)                                  
|- - ------  for And(t > -oo, t < oo, t != 0)
$$\begin{cases} - \frac{\cos{\left(t \right)}}{t} + \frac{1}{t} & \text{for}\: t > -\infty \wedge t < \infty \wedge t \neq 0 \\0 & \text{otherwise} \end{cases}$$ 
Piecewise((1/t - cos(t)/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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