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Solving integrals/ sin(3x-5)dx

Integral of sin(3x-5)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  0                
  /                
 |                 
 |  sin(3*x - 5) dx
 |                 
/                  
-pi
$$\int\limits_{- \pi}^{0} \sin{\left(3 x - 5 \right)}\, dx$$ 
Integral(sin(3*x - 5), (x, -pi, 0))
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(3*x - 5)
 | sin(3*x - 5) dx = C - ------------
 |                            3      
/
$$\int \sin{\left(3 x - 5 \right)}\, dx = C - \frac{\cos{\left(3 x - 5 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-2*cos(5)
---------
    3
$$- \frac{2 \cos{\left(5 \right)}}{3}$$ 
=
= 
-2*cos(5)
---------
    3
$$- \frac{2 \cos{\left(5 \right)}}{3}$$ 
-2*cos(5)/3
Numerical answer [src] 
-0.189108123642151
-0.189108123642151

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

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