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Solving integrals/ cos(5-3*x)

Integral of cos(5-3*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  cos(5 - 3*x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \cos{\left(5 - 3 x \right)}\, dx$$ 
Integral(cos(5 - 3*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(-5 + 3*x)
 | cos(5 - 3*x) dx = C + -------------
 |                             3      
/
$$\int \cos{\left(5 - 3 x \right)}\, dx = C + \frac{\sin{\left(3 x - 5 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  sin(2)   sin(5)
- ------ + ------
    3        3
$$\frac{\sin{\left(5 \right)}}{3} - \frac{\sin{\left(2 \right)}}{3}$$ 
=
= 
  sin(2)   sin(5)
- ------ + ------
    3        3
$$\frac{\sin{\left(5 \right)}}{3} - \frac{\sin{\left(2 \right)}}{3}$$ 
-sin(2)/3 + sin(5)/3
Numerical answer [src] 
-0.62274056716294
-0.62274056716294

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

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