Integral of -2cos2x dx

The solution

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

$$\int\limits_{x}^{\frac{\pi}{4}} \left(- 2 \cos{\left(2 x \right)}\right)\, dx$$

Integral(-2*cos(2*x), (x, x, pi/4))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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 | -2*cos(2*x) dx = C - sin(2*x)
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$$-\sin \left(2\,x\right)$$

Simplify

The answer [src]

-1 + sin(2*x)

$$-2\,\left({{\sin \left({{\pi}\over{2}}\right)}\over{2}}-{{\sin \left(2\,x\right)}\over{2}}\right)$$

-1 + sin(2*x)

$$\sin{\left(2 x \right)} - 1$$

Simplify

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

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Integral of -2cos2x dx

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