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2*cos(2*x)

Integral of 2*cos(2*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
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$$\int\limits_{0}^{\frac{\pi}{6}} 2 \cos{\left(2 x \right)}\, dx$$
Integral(2*cos(2*x), (x, 0, pi/6))
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 cosine is sine:

        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(2*x) dx = C + sin(2*x)
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$$\sin \left(2\,x\right)$$
The graph
The answer [src]
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\/ 3 
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$$\frac{\sqrt{3}}{2}$$
=
=
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\/ 3 
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  2  
$$\frac{\sqrt{3}}{2}$$
Numerical answer [src]
0.866025403784439
0.866025403784439
The graph
Integral of 2*cos(2*x) dx

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