Mister Exam

Other calculators

Solving integrals/ cos(a*x)

Integral of cos(a*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

    © Mister Exam – Calculator