Mister Exam

Integral of -sin(2*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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