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sin(x/3)
Solving integrals/ sin(x/3)

Integral of sin(x/3) dx

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The solution

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∫0πsin⁡(x3) dx\int\limits_{0}^{\pi} \sin{\left(\frac{x}{3} \right)}\, dx 
Integral(sin(x/3), (x, 0, pi))
Detail solution

  1. Let u=x3u = \frac{x}{3}.

    Then let du=dx3du = \frac{dx}{3} and substitute 3du3 du:

    ∫3sin⁡(u) du\int 3 \sin{\left(u \right)}\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫sin⁡(u) du=3∫sin⁡(u) du\int \sin{\left(u \right)}\, du = 3 \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: −3cos⁡(u)- 3 \cos{\left(u \right)}

    Now substitute uu back in:

    −3cos⁡(x3)- 3 \cos{\left(\frac{x}{3} \right)}

  2. Now simplify:

    −3cos⁡(x3)- 3 \cos{\left(\frac{x}{3} \right)}

  3. Add the constant of integration:

    −3cos⁡(x3)+constant- 3 \cos{\left(\frac{x}{3} \right)}+ \mathrm{constant}

The answer is:

−3cos⁡(x3)+constant- 3 \cos{\left(\frac{x}{3} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫sin⁡(x3) dx=C−3cos⁡(x3)\int \sin{\left(\frac{x}{3} \right)}\, dx = C - 3 \cos{\left(\frac{x}{3} \right)}
Simplify
The graph
0.000.250.500.751.001.251.501.752.002.252.502.753.005-5
Plot the graph f(x)
The answer [src] 
3/2
32\frac{3}{2} 
=
= 
3/2
32\frac{3}{2} 
3/2
Numerical answer [src] 
1.5
1.5
The graph
Integral of sin(x/3) dx

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

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