Mister Exam

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Integral of d{x}:
Integral of x*2^(-x)
Integral of ex^2
Integral of (1/x^2)dx
Integral of x*cos(x/2)
Identical expressions
two /cost^ two
2 divide by co sinus of e of t squared
two divide by co sinus of e of t to the power of two
2/cost2
2/cost²
2/cost to the power of 2
2 divide by cost^2

Solving integrals/ 2/cost^2

Integral of 2/cost^2 dt

The solution

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 pi           
 --           
 4            
  /           
 |            
 |     2      
 |  ------- dt
 |     2      
 |  cos (t)   
 |            
/             
0

$$\int\limits_{0}^{\frac{\pi}{4}} \frac{2}{\cos^{2}{\left(t \right)}}\, dt$$

Integral(2/cos(t)^2, (t, 0, pi/4))

Detail solution

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

$\int \frac{2}{\cos^{2}{\left(t \right)}}\, dt = 2 \int \frac{1}{\cos^{2}{\left(t \right)}}\, dt$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\frac{\sin{\left(t \right)}}{\cos{\left(t \right)}}$
So, the result is: $\frac{2 \sin{\left(t \right)}}{\cos{\left(t \right)}}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                         
 |                          
 |    2             2*sin(t)
 | ------- dt = C + --------
 |    2              cos(t) 
 | cos (t)                  
 |                          
/

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

Simplify

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Plot the graph f(x)

The answer [src]

$$2$$

Numerical answer [src]

2.0

2.0

The graph

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

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Identical expressions

Integral of 2/cost^2 dt

Limits of integration:

The graph:

Piecewise:

The solution