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cos(4x-3)dx
Solving integrals/ cos(4x-3)dx

Integral of cos(4x-3)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  cos(4*x - 3) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \cos{\left(4 x - 3 \right)}\, dx$$ 
Integral(cos(4*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(4*x - 3)
 | cos(4*x - 3) dx = C + ------------
 |                            4      
/
$$\int \cos{\left(4 x - 3 \right)}\, dx = C + \frac{\sin{\left(4 x - 3 \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
sin(1)   sin(3)
------ + ------
  4        4
$$\frac{\sin{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)}}{4}$$ 
=
= 
sin(1)   sin(3)
------ + ------
  4        4
$$\frac{\sin{\left(3 \right)}}{4} + \frac{\sin{\left(1 \right)}}{4}$$ 
sin(1)/4 + sin(3)/4
Numerical answer [src] 
0.245647748216941
0.245647748216941
The graph
Integral of cos(4x-3)dx dx

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

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