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Solving integrals/ cos(npix/l)

Integral of cos(npix/l) dx

Limits of integration:

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Piecewise:

The solution

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

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

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