Mister Exam

Integral of sen2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |  sin(2*x) dx
 |             
/              
0              
$$\int\limits_{0}^{1} \sin{\left(2 x \right)}\, dx$$
Integral(sin(2*x), (x, 0, 1))
Detail solution
  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:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                   cos(2*x)
 | sin(2*x) dx = C - --------
 |                      2    
/                            
$$\int \sin{\left(2 x \right)}\, dx = C - \frac{\cos{\left(2 x \right)}}{2}$$
The graph
The answer [src]
1   cos(2)
- - ------
2     2   
$$\frac{1}{2} - \frac{\cos{\left(2 \right)}}{2}$$
=
=
1   cos(2)
- - ------
2     2   
$$\frac{1}{2} - \frac{\cos{\left(2 \right)}}{2}$$
1/2 - cos(2)/2
Numerical answer [src]
0.708073418273571
0.708073418273571
The graph
Integral of sen2x dx

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