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Identical expressions
(cos20x-20sinx)
( co sinus of e of 20x minus 20 sinus of x)
cos20x-20sinx
(cos20x-20sinx)dx
Similar expressions
(cos20x+20sinx)

Integral of (cos20x-20sinx) dx

The solution

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  1                           
  /                           
 |                            
 |  (cos(20*x) - 20*sin(x)) dx
 |                            
/                             
0

$$\int\limits_{0}^{1} \left(- 20 \sin{\left(x \right)} + \cos{\left(20 x \right)}\right)\, dx$$

Integral(cos(20*x) - 20*sin(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 20 \sin{\left(x \right)}\right)\, dx = - 20 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $20 \cos{\left(x \right)}$
1. Let $u = 20 x$ .
  
  Then let $du = 20 dx$ and substitute $\frac{du}{20}$ :
  
  $\int \frac{\cos{\left(u \right)}}{20}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{20}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{20}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(20 x \right)}}{20}$
The result is: $\frac{\sin{\left(20 x \right)}}{20} + 20 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{\sin{\left(20 x \right)}}{20} + 20 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(20 x \right)}}{20} + 20 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                      
 |                                              sin(20*x)
 | (cos(20*x) - 20*sin(x)) dx = C + 20*cos(x) + ---------
 |                                                  20   
/

$$\int \left(- 20 \sin{\left(x \right)} + \cos{\left(20 x \right)}\right)\, dx = C + \frac{\sin{\left(20 x \right)}}{20} + 20 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                  sin(20)
-20 + 20*cos(1) + -------
                     20

$$-20 + \frac{\sin{\left(20 \right)}}{20} + 20 \cos{\left(1 \right)}$$

                  sin(20)
-20 + 20*cos(1) + -------
                     20

$$-20 + \frac{\sin{\left(20 \right)}}{20} + 20 \cos{\left(1 \right)}$$

-20 + 20*cos(1) + sin(20)/20

Numerical answer [src]

-9.14830662010082

-9.14830662010082

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

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Identical expressions

Similar expressions

Integral of (cos20x-20sinx) dx

Limits of integration:

The graph:

Piecewise:

The solution