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sin(0,5x)
Solving integrals/ sin(0,5x)

Integral of sin(0,5x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
 pi          
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0
∫0π3sin⁡(x2) dx\int\limits_{0}^{\frac{\pi}{3}} \sin{\left(\frac{x}{2} \right)}\, dx
Simplify
Detail solution

  1. Let u=x2u = \frac{x}{2}.

    Then let du=dx2du = \frac{dx}{2} and substitute 2du2 du:

    ∫4sin⁡(u) 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:

      ∫2sin⁡(u) du=2∫sin⁡(u) du\int 2 \sin{\left(u \right)}\, du = 2 \int \sin{\left(u \right)}\, du

      1. The integral of sine is negative cosine:

        ∫sin⁡(u) du=−cos⁡(u)\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}

      So, the result is: −2cos⁡(u)- 2 \cos{\left(u \right)}

    Now substitute uu back in:

    −2cos⁡(x2)- 2 \cos{\left(\frac{x}{2} \right)}

  2. Add the constant of integration:

    −2cos⁡(x2)+constant- 2 \cos{\left(\frac{x}{2} \right)}+ \mathrm{constant}

The answer is:

−2cos⁡(x2)+constant- 2 \cos{\left(\frac{x}{2} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                        
 |                         
 |    /x\               /x\
 | sin|-| dx = C - 2*cos|-|
 |    \2/               \2/
 |                         
/
−2 cos⁡(x2)-2\,\cos \left({{x}\over{2}}\right)
Simplify
The graph
0.000.100.200.300.400.500.600.700.800.901.002.5-2.5
Plot the graph f(x)
The answer [src] 
      ___
2 - \/ 3
−3+2- \sqrt{3} + 2 
=
= 
      ___
2 - \/ 3
−3+2- \sqrt{3} + 2
Simplify
Numerical answer [src] 
0.267949192431123
0.267949192431123
The graph
Integral of sin(0,5x) dx

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

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