Mister Exam

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How to use it?
Integral of d{x}:
Integral of 1/(x^2+3x+2)
Integral of cosecx
Integral of sin(e^x)
Integral of log(x)^3/x
Graphing y =:
2*cos(x)
Derivative of:
2*cos(x)
Limit of the function:
2*cos(x)
Identical expressions
two *cos(x)
2 multiply by co sinus of e of (x)
two multiply by co sinus of e of (x)
2cos(x)
2cosx
2*cos(x)dx
Similar expressions
-2cosx
sqrt(1-2cosx+2cos(x)^2)
sinx/√(3+2cosx)
sinx^2*cosx
3x^2cosx^3
2*cosx

Solving integrals/ 2*cos(x)

Integral of 2*cos(x) dx

The solution

You have entered [src]

  x            
  -            
  2            
  /            
 |             
 |  2*cos(x) dx
 |             
/              
0

$$\int\limits_{0}^{\frac{x}{2}} 2 \cos{\left(x \right)}\, dx$$

Integral(2*cos(x), (x, 0, x/2))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 2 \cos{\left(x \right)}\, dx = 2 \int \cos{\left(x \right)}\, dx$
1. The integral of cosine is sine:
  
  $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
So, the result is: $2 \sin{\left(x \right)}$
Add the constant of integration:

$2 \sin{\left(x \right)}+ \mathrm{constant}$

The answer is:

$2 \sin{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                           
 | 2*cos(x) dx = C + 2*sin(x)
 |                           
/

$$\int 2 \cos{\left(x \right)}\, dx = C + 2 \sin{\left(x \right)}$$

Simplify

The answer [src]

     /x\
2*sin|-|
     \2/

$$2 \sin{\left(\frac{x}{2} \right)}$$

=

     /x\
2*sin|-|
     \2/

$$2 \sin{\left(\frac{x}{2} \right)}$$

2*sin(x/2)

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