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Integral of 2*sin(3*x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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 |  2*sin(3*x) dx
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$$\int\limits_{0}^{0} 2 \sin{\left(3 x \right)}\, dx$$
Integral(2*sin(3*x), (x, 0, 0))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

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

        1. The integral of sine is negative cosine:

        So, the result is:

      Now substitute back in:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
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 |                     2*cos(3*x)
 | 2*sin(3*x) dx = C - ----------
 |                         3     
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$$\int 2 \sin{\left(3 x \right)}\, dx = C - \frac{2 \cos{\left(3 x \right)}}{3}$$
The graph
The answer [src]
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.