Mister Exam

Integral of cos(-2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                           
 |                    sin(2*x)
 | cos(-2*x) dx = C + --------
 |                       2    
/                             
$$\int \cos{\left(- 2 x \right)}\, dx = C + \frac{\sin{\left(2 x \right)}}{2}$$
The graph
The answer [src]
sin(2)
------
  2   
$$\frac{\sin{\left(2 \right)}}{2}$$
=
=
sin(2)
------
  2   
$$\frac{\sin{\left(2 \right)}}{2}$$
sin(2)/2
Numerical answer [src]
0.454648713412841
0.454648713412841

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