Mister Exam

Integral of sin(nx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |  sin(n*x) dx
 |             
/              
0              
$$\int\limits_{0}^{1} \sin{\left(n x \right)}\, dx$$
The answer (Indefinite) [src]
  /                  //-cos(n*x)             \
 |                   ||----------  for n != 0|
 | sin(n*x) dx = C + |<    n                 |
 |                   ||                      |
/                    \\    0       otherwise /
$$-{{\cos \left(n\,x\right)}\over{n}}$$
The answer [src]
/1   cos(n)                                  
|- - ------  for And(n > -oo, n < oo, n != 0)

            
$${{1}\over{n}}-{{\cos n}\over{n}}$$
=
=
/1   cos(n)                                  
|- - ------  for And(n > -oo, n < oo, n != 0)

            
$$\begin{cases} - \frac{\cos{\left(n \right)}}{n} + \frac{1}{n} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}$$

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