Mister Exam

Other calculators

Solving integrals/ 4*cos(8*x+5)

Integral of 4*cos(8*x+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |  4*cos(8*x + 5) dx
 |                   
/                    
0
$$\int\limits_{0}^{1} 4 \cos{\left(8 x + 5 \right)}\, dx$$ 
Integral(4*cos(8*x + 5), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of cosine is sine:

        So, the result is:

      Now substitute back in:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                    
 |                         sin(8*x + 5)
 | 4*cos(8*x + 5) dx = C + ------------
 |                              2      
/
$$\int 4 \cos{\left(8 x + 5 \right)}\, dx = C + \frac{\sin{\left(8 x + 5 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
sin(13)   sin(5)
------- - ------
   2        2
$$\frac{\sin{\left(13 \right)}}{2} - \frac{\sin{\left(5 \right)}}{2}$$ 
=
= 
sin(13)   sin(5)
------- - ------
   2        2
$$\frac{\sin{\left(13 \right)}}{2} - \frac{\sin{\left(5 \right)}}{2}$$ 
sin(13)/2 - sin(5)/2
Numerical answer [src] 
0.68954565574489
0.68954565574489

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

    © Mister Exam – Calculator