Integral of 4cos2xdx dx

The solution

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 |  4*cos(2*x) dx
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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

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

$\int 4 \cos{\left(2 x \right)}\, dx = 4 \int \cos{\left(2 x \right)}\, dx$
1. Let $u = 2 x$ .
  
  Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
  
  $\int \frac{\cos{\left(u \right)}}{2}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{2}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{2}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(2 x \right)}}{2}$
So, the result is: $2 \sin{\left(2 x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                              
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 | 4*cos(2*x) dx = C + 2*sin(2*x)
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$$\int 4 \cos{\left(2 x \right)}\, dx = C + 2 \sin{\left(2 x \right)}$$

Simplify

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.

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Identical expressions

Integral of 4cos2xdx dx

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The solution