Mister exam

Other calculators

Integral sin(npix/l) dx

Limits of integration:

from to

The graph:

from to

Enter:

The solution

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

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

    To see a detailed solution - share to all your student friends
    To see a detailed solution,
    share to all your student friends: