Mister Exam

Integral of 4cos2xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  p              
  -              
  2              
  /              
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 |  4*cos(2*x) dx
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p                
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4                
$$\int\limits_{\frac{p}{4}}^{\frac{p}{2}} 4 \cos{\left(2 x \right)}\, dx$$
Integral(4*cos(2*x), (x, p/4, p/2))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    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:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                              
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 | 4*cos(2*x) dx = C + 2*sin(2*x)
 |                               
/                                
$$\int 4 \cos{\left(2 x \right)}\, dx = C + 2 \sin{\left(2 x \right)}$$
The answer [src]
       /p\           
- 2*sin|-| + 2*sin(p)
       \2/           
$$- 2 \sin{\left(\frac{p}{2} \right)} + 2 \sin{\left(p \right)}$$
=
=
       /p\           
- 2*sin|-| + 2*sin(p)
       \2/           
$$- 2 \sin{\left(\frac{p}{2} \right)} + 2 \sin{\left(p \right)}$$
-2*sin(p/2) + 2*sin(p)

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