Mister Exam

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Identical expressions
п/ zero ^8cos4xdx
п divide by 0 to the power of 8 co sinus of e of 4xdx
п divide by zero to the power of 8 co sinus of e of 4xdx
п/08cos4xdx
п/0⁸cos4xdx
п divide by 0^8cos4xdx

Integral of п/0^8cos4xdx dx

The solution

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  1               
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 |  pi            
 |  --*cos(4*x) dx
 |  0             
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0

$$\int\limits_{0}^{1} \frac{\pi}{0} \cos{\left(4 x \right)}\, dx$$

Integral((pi/0)*cos(4*x), (x, 0, 1))

Detail solution

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

$\int \frac{\pi}{0} \cos{\left(4 x \right)}\, dx = \tilde{\infty} \int \cos{\left(4 x \right)}\, dx$
1. Let $u = 4 x$ .
  
  Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :
  
  $\int \frac{\cos{\left(u \right)}}{4}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{4}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(4 x \right)}}{4}$
So, the result is: $\tilde{\infty} \sin{\left(4 x \right)}$
Add the constant of integration:

$\tilde{\infty} \sin{\left(4 x \right)}+ \mathrm{constant}$

The answer is:

$\tilde{\infty} \sin{\left(4 x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
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 | pi                               
 | --*cos(4*x) dx = C + zoo*sin(4*x)
 | 0                                
 |                                  
/

$$\int \frac{\pi}{0} \cos{\left(4 x \right)}\, dx = C + \tilde{\infty} \sin{\left(4 x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

      1            
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zoo* |  cos(4*x) dx
     |             
    /              
    0

$$\tilde{\infty} \int\limits_{0}^{1} \cos{\left(4 x \right)}\, dx$$

      1            
      /            
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zoo* |  cos(4*x) dx
     |             
    /              
    0

$$\tilde{\infty} \int\limits_{0}^{1} \cos{\left(4 x \right)}\, dx$$

±oo*Integral(cos(4*x), (x, 0, 1))

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

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Identical expressions

Integral of п/0^8cos4xdx dx

Limits of integration:

The graph:

Piecewise:

The solution