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Identical expressions
zero . five *cos((two * three . fourteen *t)/ zero . three hundred and twenty-five)
0.005 multiply by co sinus of e of ((2 multiply by 3.14 multiply by t) divide by 0.0325)
zero . five multiply by co sinus of e of ((two multiply by three . fourteen multiply by t) divide by zero . three hundred and twenty minus five)
0.005cos((23.14t)/0.0325)
0.005cos23.14t/0.0325
0.005*cos((2*3.14*t) divide by 0.0325)

Solving integrals/ 0.005*cos((2*3.14*t)/0.0325)

Integral of 0.005cos((23.14*t)/0.0325) dt

The solution

You have entered [src]

 1/500                      
   /                        
  |                         
  |      /  157     1   \   
  |   cos|2*---*t*------|   
  |      \   50   0.0325/   
  |   ------------------- dt
  |           200           
  |                         
 /                          
 0

$$\int\limits_{0}^{\frac{1}{500}} \frac{\cos{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}}{200}\, dt$$

Integral(cos(2*(157/50)*t/0.0325)/200, (t, 0, 1/500))

Detail solution

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

$\int \frac{\cos{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}}{200}\, dt = \frac{\int \cos{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}\, dt}{200}$
1. Let $u = 2 \cdot \frac{157}{50} t \frac{1}{0.0325}$ .
  
  Then let $du = 193.230769230769 dt$ and substitute $0.00517515923566879 du$ :
  
  $\int 2.6782273114528 \cdot 10^{-5} \cos{\left(u \right)}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 0.00517515923566879 \cos{\left(u \right)}\, du = 0.00517515923566879 \int \cos{\left(u \right)}\, du$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $0.00517515923566879 \sin{\left(u \right)}$
  Now substitute $u$ back in:
  
  $0.00517515923566879 \sin{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}$
So, the result is: $2.58757961783439 \cdot 10^{-5} \sin{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}$
Now simplify:

$2.58757961783439 \cdot 10^{-5} \sin{\left(193.230769230769 t \right)}$
Add the constant of integration:

$2.58757961783439 \cdot 10^{-5} \sin{\left(193.230769230769 t \right)}+ \mathrm{constant}$

The answer is:

$2.58757961783439 \cdot 10^{-5} \sin{\left(193.230769230769 t \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                    
 |                                                                     
 |    /  157     1   \                                                 
 | cos|2*---*t*------|                                                 
 |    \   50   0.0325/                                 /  157     1   \
 | ------------------- dt = C + 2.58757961783439e-5*sin|2*---*t*------|
 |         200                                         \   50   0.0325/
 |                                                                     
/

$$\int \frac{\cos{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}}{200}\, dt = C + 2.58757961783439 \cdot 10^{-5} \sin{\left(2 \cdot \frac{157}{50} t \frac{1}{0.0325} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

9.75293138371004e-6

$$9.75293138371004 \cdot 10^{-6}$$

9.75293138371004e-6

$$9.75293138371004 \cdot 10^{-6}$$

Упростить

Numerical answer [src]

9.75293138371004e-6

9.75293138371004e-6

The graph

Integral of 0.005*cos((2*3.14*t)/0.0325) dt

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

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Identical expressions

Integral of 0.005cos((23.14*t)/0.0325) dt

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Integral of 0.005*cos((2*3.14*t)/0.0325) dt

Limits of integration:

The graph:

Piecewise:

The solution

Integral of 0.005cos((23.14*t)/0.0325) dt