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Solving integrals/ sin(1-5*x)dx

Integral of sin(1-5*x)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  sin(1 - 5*x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \sin{\left(1 - 5 x \right)}\, dx$$ 
Integral(sin(1 - 5*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 sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                       cos(-1 + 5*x)
 | sin(1 - 5*x) dx = C + -------------
 |                             5      
/
$$\int \sin{\left(1 - 5 x \right)}\, dx = C + \frac{\cos{\left(5 x - 1 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  cos(1)   cos(4)
- ------ + ------
    5        5
$$\frac{\cos{\left(4 \right)}}{5} - \frac{\cos{\left(1 \right)}}{5}$$ 
=
= 
  cos(1)   cos(4)
- ------ + ------
    5        5
$$\frac{\cos{\left(4 \right)}}{5} - \frac{\cos{\left(1 \right)}}{5}$$ 
-cos(1)/5 + cos(4)/5
Numerical answer [src] 
-0.23878918534635
-0.23878918534635

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

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