Mister Exam

Integral of 3sin2x de

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |  3*sin(2*x) dx
 |               
/                
0                
$$\int\limits_{0}^{1} 3 \sin{\left(2 x \right)}\, dx$$
Integral(3*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]
  /                              
 |                     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*cos(2)
- - --------
2      2    
$$\frac{3}{2} - \frac{3 \cos{\left(2 \right)}}{2}$$
=
=
3   3*cos(2)
- - --------
2      2    
$$\frac{3}{2} - \frac{3 \cos{\left(2 \right)}}{2}$$
3/2 - 3*cos(2)/2
Numerical answer [src]
2.12422025482071
2.12422025482071

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