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sin(x/2)
Solving integrals/ sin(x/2)

Integral of sin(x/2) dx

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The solution

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∫01sin⁡(x2) dx\int\limits_{0}^{1} \sin{\left(\frac{x}{2} \right)}\, dx 
Integral(sin(x/2), (x, 0, 1))
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. Now simplify:

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

  3. 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] 
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∫sin⁡(x2) dx=C−2cos⁡(x2)\int \sin{\left(\frac{x}{2} \right)}\, dx = C - 2 \cos{\left(\frac{x}{2} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Plot the graph f(x)
The answer [src] 
2 - 2*cos(1/2)
2−2cos⁡(12)2 - 2 \cos{\left(\frac{1}{2} \right)} 
=
= 
2 - 2*cos(1/2)
2−2cos⁡(12)2 - 2 \cos{\left(\frac{1}{2} \right)}
Упростить
Numerical answer [src] 
0.244834876219255
0.244834876219255
The graph
Integral of sin(x/2) dx

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

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