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Solving integrals/ cos(3*x)

Integral of cos(3*x) dx

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 |  cos(3*x) dx
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$$\int\limits_{0}^{1} \cos{\left(3 x \right)}\, dx$$

Integral(cos(3*x), (x, 0, 1))

Detail solution

Let $u = 3 x$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{\cos{\left(u \right)}}{3}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{3}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{3}$
Now substitute $u$ back in:

$\frac{\sin{\left(3 x \right)}}{3}$
Add the constant of integration:

$\frac{\sin{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                   sin(3*x)
 | cos(3*x) dx = C + --------
 |                      3    
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$$\int \cos{\left(3 x \right)}\, dx = C + \frac{\sin{\left(3 x \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(3)
------
  3

$$\frac{\sin{\left(3 \right)}}{3}$$

sin(3)
------
  3

$$\frac{\sin{\left(3 \right)}}{3}$$

sin(3)/3

Numerical answer [src]

0.0470400026866224

0.0470400026866224

The graph

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