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Integral of sin(10*x) dx

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 3/10            
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  |  sin(10*x) dx
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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

Let $u = 10 x$ .

Then let $du = 10 dx$ and substitute $\frac{du}{10}$ :

$\int \frac{\sin{\left(u \right)}}{10}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{10}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{10}$
Now substitute $u$ back in:

$- \frac{\cos{\left(10 x \right)}}{10}$
Add the constant of integration:

$- \frac{\cos{\left(10 x \right)}}{10}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(10 x \right)}}{10}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                    cos(10*x)
 | sin(10*x) dx = C - ---------
 |                        10   
/

$$\int \sin{\left(10 x \right)}\, dx = C - \frac{\cos{\left(10 x \right)}}{10}$$

Simplify

The graph

Plot the graph f(x)

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.