Mister Exam

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Identical expressions
(one - one /sin^2x)
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(one minus one divide by sinus of squared x)
(1-1/sin2x)
1-1/sin2x
(1-1/sin²x)
(1-1/sin to the power of 2x)
1-1/sin^2x
(1-1 divide by sin^2x)
(1-1/sin^2x)dx
Similar expressions
(1+1/sin^2x)

Integral of (1-1/sin^2x) dx

The solution

You have entered [src]

 157                
 ---                
 100                
  /                 
 |                  
 |  /       1   \   
 |  |1 - -------| dx
 |  |       2   |   
 |  \    sin (x)/   
 |                  
/                   
157                 
---                 
300

$$\int\limits_{\frac{157}{300}}^{\frac{157}{100}} \left(1 - \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx$$

Integral(1 - 1/sin(x)^2, (x, 157/300, 157/100))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = - \int \frac{1}{\sin^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
  So, the result is: $\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $x + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$x + \frac{1}{\tan{\left(x \right)}}$
Add the constant of integration:

$x + \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$x + \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                                  
 | /       1   \              cos(x)
 | |1 - -------| dx = C + x + ------
 | |       2   |              sin(x)
 | \    sin (x)/                    
 |                                  
/

$$\int \left(1 - \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = C + x + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         /157\      /157\
      cos|---|   cos|---|
157      \100/      \300/
--- + -------- - --------
150      /157\      /157\
      sin|---|   sin|---|
         \100/      \300/

$$- \frac{\cos{\left(\frac{157}{300} \right)}}{\sin{\left(\frac{157}{300} \right)}} + \frac{\cos{\left(\frac{157}{100} \right)}}{\sin{\left(\frac{157}{100} \right)}} + \frac{157}{150}$$

         /157\      /157\
      cos|---|   cos|---|
157      \100/      \300/
--- + -------- - --------
150      /157\      /157\
      sin|---|   sin|---|
         \100/      \300/

$$- \frac{\cos{\left(\frac{157}{300} \right)}}{\sin{\left(\frac{157}{300} \right)}} + \frac{\cos{\left(\frac{157}{100} \right)}}{\sin{\left(\frac{157}{100} \right)}} + \frac{157}{150}$$

157/150 + cos(157/100)/sin(157/100) - cos(157/300)/sin(157/300)

Numerical answer [src]

-0.685650071406749

-0.685650071406749

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

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Identical expressions

Similar expressions

Integral of (1-1/sin^2x) dx

Limits of integration:

The graph:

Piecewise:

The solution