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Solving integrals/ sin(n*pi*x)/l

Integral of sin(n*pi*x)/l dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

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