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Solving integrals/ 2cos2t

Integral of 2cos2t dx

The solution

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 |  2*cos(2*t) dt
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$$\int\limits_{0}^{1} 2 \cos{\left(2 t \right)}\, dt$$

Integral(2*cos(2*t), (t, 0, 1))

Detail solution

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

$\int 2 \cos{\left(2 t \right)}\, dt = 2 \int \cos{\left(2 t \right)}\, dt$
1. Let $u = 2 t$ .
  
  Then let $du = 2 dt$ 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:
  
  $\frac{\sin{\left(2 t \right)}}{2}$
So, the result is: $\sin{\left(2 t \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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 | 2*cos(2*t) dt = C + sin(2*t)
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$$\int 2 \cos{\left(2 t \right)}\, dt = C + \sin{\left(2 t \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(2)

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

=

sin(2)

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

sin(2)

Numerical answer [src]

0.909297426825682

0.909297426825682

The graph

Integral of 2cos2t dx

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