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Integral of sin(10*x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
 3/10            
   /             
  |              
  |  sin(10*x) dx
  |              
 /               
1/10             
$$\int\limits_{\frac{1}{10}}^{\frac{3}{10}} \sin{\left(10 x \right)}\, dx$$
Integral(sin(10*x), (x, 1/10, 3/10))
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. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
 |                    cos(10*x)
 | sin(10*x) dx = C - ---------
 |                        10   
/                              
$$\int \sin{\left(10 x \right)}\, dx = C - \frac{\cos{\left(10 x \right)}}{10}$$
The graph
The answer [src]
  cos(3)   cos(1)
- ------ + ------
    10       10  
$$\frac{\cos{\left(1 \right)}}{10} - \frac{\cos{\left(3 \right)}}{10}$$
=
=
  cos(3)   cos(1)
- ------ + ------
    10       10  
$$\frac{\cos{\left(1 \right)}}{10} - \frac{\cos{\left(3 \right)}}{10}$$
-cos(3)/10 + cos(1)/10
Numerical answer [src]
0.153029480246859
0.153029480246859

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