Integral of cos(2*t) dx

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

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

Detail solution

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:

$\frac{\sin{\left(2 t \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(2)
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  2

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

sin(2)
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  2

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

sin(2)/2

Numerical answer [src]

0.454648713412841

0.454648713412841

The graph

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