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Integral of d{x}:
Integral of x*arctan(3x)
Integral of cos(pi*x/3)
Integral of yx^2
Integral of tan³xsecx
Derivative of:
cos(pi*x/3)
Limit of the function:
cos(pi*x/3)
Identical expressions
cos(pi*x/ three)
co sinus of e of ( Pi multiply by x divide by 3)
co sinus of e of ( Pi multiply by x divide by three)
cos(pix/3)
cospix/3
cos(pi*x divide by 3)
cos(pi*x/3)dx

Integral of cos(pi*x/3) dx

The solution

You have entered [src]

  1             
  /             
 |              
 |     /pi*x\   
 |  cos|----| dx
 |     \ 3  /   
 |              
/               
0

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

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

Detail solution

Let $u = \frac{\pi x}{3}$ .

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

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

$\frac{3 \sin{\left(\frac{\pi x}{3} \right)}}{\pi}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                        /pi*x\
 |                    3*sin|----|
 |    /pi*x\               \ 3  /
 | cos|----| dx = C + -----------
 |    \ 3  /               pi    
 |                               
/

$$\int \cos{\left(\frac{\pi x}{3} \right)}\, dx = C + \frac{3 \sin{\left(\frac{\pi x}{3} \right)}}{\pi}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ___
3*\/ 3 
-------
  2*pi

$$\frac{3 \sqrt{3}}{2 \pi}$$

    ___
3*\/ 3 
-------
  2*pi

$$\frac{3 \sqrt{3}}{2 \pi}$$

3*sqrt(3)/(2*pi)

Numerical answer [src]

0.826993343132688

0.826993343132688

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

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Identical expressions

Integral of cos(pi*x/3) dx

Limits of integration:

The graph:

Piecewise:

The solution