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Integral of (sin5x-sin5a) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                         
  /                         
 |                          
 |  (sin(5*x) - sin(5*a)) dx
 |                          
/                           
0                           
$$\int\limits_{0}^{1} \left(- \sin{\left(5 a \right)} + \sin{\left(5 x \right)}\right)\, dx$$
Integral(sin(5*x) - sin(5*a), (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

    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:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                    
 |                                cos(5*x)             
 | (sin(5*x) - sin(5*a)) dx = C - -------- - x*sin(5*a)
 |                                   5                 
/                                                      
$$\int \left(- \sin{\left(5 a \right)} + \sin{\left(5 x \right)}\right)\, dx = C - x \sin{\left(5 a \right)} - \frac{\cos{\left(5 x \right)}}{5}$$
The answer [src]
1              cos(5)
- - sin(5*a) - ------
5                5   
$$- \sin{\left(5 a \right)} - \frac{\cos{\left(5 \right)}}{5} + \frac{1}{5}$$
=
=
1              cos(5)
- - sin(5*a) - ------
5                5   
$$- \sin{\left(5 a \right)} - \frac{\cos{\left(5 \right)}}{5} + \frac{1}{5}$$
1/5 - sin(5*a) - cos(5)/5

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