Integral of sin(0,5x) dx

The solution

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$$\int\limits_{0}^{\frac{\pi}{3}} \sin{\left(\frac{x}{2} \right)}\, dx$$

Simplify

Detail solution

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

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

$\int 4 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sin{\left(u \right)}\, du = 2 \int \sin{\left(u \right)}\, du$
  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:

$- 2 \cos{\left(\frac{x}{2} \right)}$
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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$$-2\,\cos \left({{x}\over{2}}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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2 - \/ 3

$$- \sqrt{3} + 2$$

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2 - \/ 3

$$- \sqrt{3} + 2$$

Simplify

Numerical answer [src]

0.267949192431123

0.267949192431123

The graph

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

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Integral of sin(0,5x) dx

Limits of integration:

The graph:

Piecewise:

The solution