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Solving integrals/ cos(19*x)

Integral of cos(19*x) dx

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 |  cos(19*x) dx
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0

$$\int\limits_{0}^{1} \cos{\left(19 x \right)}\, dx$$

Integral(cos(19*x), (x, 0, 1))

Detail solution

Let $u = 19 x$ .

Then let $du = 19 dx$ and substitute $\frac{du}{19}$ :

$\int \frac{\cos{\left(u \right)}}{361}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(u \right)}}{19}\, du = \frac{\int \cos{\left(u \right)}\, du}{19}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{19}$
Now substitute $u$ back in:

$\frac{\sin{\left(19 x \right)}}{19}$
Add the constant of integration:

$\frac{\sin{\left(19 x \right)}}{19}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(19 x \right)}}{19}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                    sin(19*x)
 | cos(19*x) dx = C + ---------
 |                        19   
/

$$\int \cos{\left(19 x \right)}\, dx = C + \frac{\sin{\left(19 x \right)}}{19}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(19)
-------
   19

$$\frac{\sin{\left(19 \right)}}{19}$$

sin(19)
-------
   19

$$\frac{\sin{\left(19 \right)}}{19}$$

Упростить

Numerical answer [src]

0.00788827419278696

0.00788827419278696

The graph

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