Mister Exam

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Integral of d{x}:
Integral of x^(-1/2)
Integral of -e^x
Integral of -xe^x
Integral of x*dx/(x^2-1)
Derivative of:
sen(x/2)
Identical expressions
sen(x/ two)
sen(x divide by 2)
sen(x divide by two)
senx/2
sen(x/2)dx

Integral of sen(x/2) dx

The solution

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 oo          
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 |  sin|-| dx
 |     \2/   
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0

$$\int\limits_{0}^{\infty} \sin{\left(\frac{x}{2} \right)}\, dx$$

Integral(sin(x/2), (x, 0, oo))

Detail solution

Let $u = \frac{x}{2}$ .

Then let $du = \frac{dx}{2}$ and substitute $2 du$ :

$\int 2 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = 2 \int \sin{\left(u \right)}\, du$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- 2 \cos{\left(u \right)}$
Now substitute $u$ back in:

$- 2 \cos{\left(\frac{x}{2} \right)}$
Now simplify:

$- 2 \cos{\left(\frac{x}{2} \right)}$
Add the constant of integration:

$- 2 \cos{\left(\frac{x}{2} \right)}+ \mathrm{constant}$

The answer is:

$- 2 \cos{\left(\frac{x}{2} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
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 |    /x\               /x\
 | sin|-| dx = C - 2*cos|-|
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$$\int \sin{\left(\frac{x}{2} \right)}\, dx = C - 2 \cos{\left(\frac{x}{2} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

<0, 4>

$$\left\langle 0, 4\right\rangle$$

<0, 4>

$$\left\langle 0, 4\right\rangle$$

AccumBounds(0, 4)

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

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How to use it?

Identical expressions

Integral of sen(x/2) dx

Limits of integration:

The graph:

Piecewise:

The solution