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sin(4x-1)
Solving integrals/ sin(4x-1)

Integral of sin(4x-1) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  sin(4*x - 1) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \sin{\left(4 x - 1 \right)}\, dx$$ 
Integral(sin(4*x - 1), (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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                       cos(4*x - 1)
 | sin(4*x - 1) dx = C - ------------
 |                            4      
/
$$\int \sin{\left(4 x - 1 \right)}\, dx = C - \frac{\cos{\left(4 x - 1 \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  cos(3)   cos(1)
- ------ + ------
    4        4
$$\frac{\cos{\left(1 \right)}}{4} - \frac{\cos{\left(3 \right)}}{4}$$ 
=
= 
  cos(3)   cos(1)
- ------ + ------
    4        4
$$\frac{\cos{\left(1 \right)}}{4} - \frac{\cos{\left(3 \right)}}{4}$$ 
-cos(3)/4 + cos(1)/4
Numerical answer [src] 
0.382573700617146
0.382573700617146
The graph
Integral of sin(4x-1) dx

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

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