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cos(x/3)
Solving integrals/ cos(x/3)

Integral of cos(x/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
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 |     /x\   
 |  cos|-| dx
 |     \3/   
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0
$$\int\limits_{0}^{1} \cos{\left(\frac{x}{3} \right)}\, dx$$ 
Integral(cos(x/3), (x, 0, 1))
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 cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                        
 |                         
 |    /x\               /x\
 | cos|-| dx = C + 3*sin|-|
 |    \3/               \3/
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/
$$\int \cos{\left(\frac{x}{3} \right)}\, dx = C + 3 \sin{\left(\frac{x}{3} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3*sin(1/3)
$$3 \sin{\left(\frac{1}{3} \right)}$$ 
=
= 
3*sin(1/3)
$$3 \sin{\left(\frac{1}{3} \right)}$$ 
3*sin(1/3)
Numerical answer [src] 
0.981584090388457
0.981584090388457
The graph
Integral of cos(x/3) dx

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

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