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2*sin(2*x)

Integral of 2*sin(2*x) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

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

    1. There are multiple ways to do this integral.

      Method #1

      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:

      Method #2

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

        1. There are multiple ways to do this integral.

          Method #1

          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 is when :

              So, the result is:

            Now substitute back in:

          Method #2

          1. Let .

            Then let and substitute :

            1. The integral of is when :

            Now substitute back in:

        So, the result is:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
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 | 2*sin(2*x) dx = C - cos(2*x)
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$$\int 2 \sin{\left(2 x \right)}\, dx = C - \cos{\left(2 x \right)}$$
The graph
The answer [src]
1 - cos(2)
$$1 - \cos{\left(2 \right)}$$
=
=
1 - cos(2)
$$1 - \cos{\left(2 \right)}$$
1 - cos(2)
Numerical answer [src]
1.41614683654714
1.41614683654714
The graph
Integral of 2*sin(2*x) dx

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