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Integral of 3*sin(2*x)*dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi              
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 |  3*sin(2*x) dx
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$$\int\limits_{0}^{\frac{\pi}{2}} 3 \sin{\left(2 x \right)}\, dx$$
Integral(3*sin(2*x), (x, 0, pi/2))
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]
  /                              
 |                     3*cos(2*x)
 | 3*sin(2*x) dx = C - ----------
 |                         2     
/                                
$$\int 3 \sin{\left(2 x \right)}\, dx = C - \frac{3 \cos{\left(2 x \right)}}{2}$$
The graph
The answer [src]
3
$$3$$
=
=
3
$$3$$
3
Numerical answer [src]
3.0
3.0

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