Mister Exam

Other calculators

Solving integrals/ cos(1-8x)dx

Integral of cos(1-8x)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  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:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                       sin(-1 + 8*x)
 | cos(1 - 8*x) dx = C + -------------
 |                             8      
/
$$\int \cos{\left(1 - 8 x \right)}\, dx = C + \frac{\sin{\left(8 x - 1 \right)}}{8}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
sin(1)   sin(7)
------ + ------
  8        8
$$\frac{\sin{\left(7 \right)}}{8} + \frac{\sin{\left(1 \right)}}{8}$$ 
=
= 
sin(1)   sin(7)
------ + ------
  8        8
$$\frac{\sin{\left(7 \right)}}{8} + \frac{\sin{\left(1 \right)}}{8}$$ 
sin(1)/8 + sin(7)/8
Numerical answer [src] 
0.187307197940836
0.187307197940836

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

    © Mister Exam – Calculator