Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin(x)*dx/x
Integral of 1/sqrt(x^2+1)
Integral of x^3*ln(x)
Integral of x*ln(x+1)dx
Graphing y =:
cos(x-pi/3)
Derivative of:
cos(x-pi/3)
Identical expressions
cos(x-pi/ three)
co sinus of e of (x minus Pi divide by 3)
co sinus of e of (x minus Pi divide by three)
cosx-pi/3
cos(x-pi divide by 3)
cos(x-pi/3)dx
Similar expressions
xcos((x-pi)/3)
cos(x+pi/3)

Integral of cos(x-pi/3) dx

The solution

You have entered [src]

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

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

Integral(cos(x - pi/3), (x, 0, pi/3))

Detail solution

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

Then let $du = dx$ and substitute $du$ :

$\int \cos{\left(u \right)}\, du$
1. The integral of cosine is sine:
  
  $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
Now substitute $u$ back in:

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

$- \cos{\left(x + \frac{\pi}{6} \right)}$
Add the constant of integration:

$- \cos{\left(x + \frac{\pi}{6} \right)}+ \mathrm{constant}$

The answer is:

$- \cos{\left(x + \frac{\pi}{6} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  ___
\/ 3 
-----
  2

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

  ___
\/ 3 
-----
  2

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

sqrt(3)/2

Numerical answer [src]

0.866025403784439

0.866025403784439

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of cos(x-pi/3) dx

Limits of integration:

The graph:

Piecewise:

The solution