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Solving integrals/ cos(10x―3)

Integral of cos(10x―3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  cos(10*x - 3) dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \cos{\left(10 x - 3 \right)}\, dx$$ 
Integral(cos(10*x - 3), (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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                    
 |                        sin(10*x - 3)
 | cos(10*x - 3) dx = C + -------------
 |                              10     
/
$$\int \cos{\left(10 x - 3 \right)}\, dx = C + \frac{\sin{\left(10 x - 3 \right)}}{10}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
sin(3)   sin(7)
------ + ------
  10       10
$$\frac{\sin{\left(3 \right)}}{10} + \frac{\sin{\left(7 \right)}}{10}$$ 
=
= 
sin(3)   sin(7)
------ + ------
  10       10
$$\frac{\sin{\left(3 \right)}}{10} + \frac{\sin{\left(7 \right)}}{10}$$ 
sin(3)/10 + sin(7)/10
Numerical answer [src] 
0.0798106606778656
0.0798106606778656

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

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