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Solving integrals/ sin(n*x)

Integral of sin(n*x) dx

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The solution

You have entered [src] 
 2*pi           
   /            
  |             
  |  sin(n*x) dx
  |             
 /              
3*pi            
----            
 2
$$\int\limits_{\frac{3 \pi}{2}}^{2 \pi} \sin{\left(n x \right)}\, dx$$ 
Integral(sin(n*x), (x, 3*pi/2, 2*pi))
The answer (Indefinite) [src] 
  /                  //-cos(n*x)             \
 |                   ||----------  for n != 0|
 | sin(n*x) dx = C + |<    n                 |
 |                   ||                      |
/                    \\    0       otherwise /
$$\int \sin{\left(n x \right)}\, dx = C + \begin{cases} - \frac{\cos{\left(n x \right)}}{n} & \text{for}\: n \neq 0 \\0 & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/   /3*pi*n\                                                
|cos|------|                                                
|   \  2   /   cos(2*pi*n)                                  
<----------- - -----------  for And(n > -oo, n < oo, n != 0)
|     n             n                                       
|                                                           
\            0                         otherwise
$$\begin{cases} \frac{\cos{\left(\frac{3 \pi n}{2} \right)}}{n} - \frac{\cos{\left(2 \pi n \right)}}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$ 
=
= 
/   /3*pi*n\                                                
|cos|------|                                                
|   \  2   /   cos(2*pi*n)                                  
<----------- - -----------  for And(n > -oo, n < oo, n != 0)
|     n             n                                       
|                                                           
\            0                         otherwise
$$\begin{cases} \frac{\cos{\left(\frac{3 \pi n}{2} \right)}}{n} - \frac{\cos{\left(2 \pi n \right)}}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$ 
Piecewise((cos(3*pi*n/2)/n - cos(2*pi*n)/n, (n > -oo)∧(n < oo)∧(Ne(n, 0))), (0, True))

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

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