Mister Exam

Other calculators

Solving integrals/ 1/sin²*2x

Integral of 1/sin²*2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi           
 --           
 4            
  /           
 |            
 |     x      
 |  ------- dx
 |     2      
 |  sin (2)   
 |            
/             
pi            
--            
8
$$\int\limits_{\frac{\pi}{8}}^{\frac{\pi}{4}} \frac{x}{\sin^{2}{\left(2 \right)}}\, dx$$ 
Integral(x/sin(2)^2, (x, pi/8, pi/4))
Detail solution

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

    1. The integral of is when :

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          
 |                       2   
 |    x                 x    
 | ------- dx = C + ---------
 |    2                  2   
 | sin (2)          2*sin (2)
 |                           
/
$$\int \frac{x}{\sin^{2}{\left(2 \right)}}\, dx = C + \frac{x^{2}}{2 \sin^{2}{\left(2 \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       2   
   3*pi    
-----------
       2   
128*sin (2)
$$\frac{3 \pi^{2}}{128 \sin^{2}{\left(2 \right)}}$$ 
=
= 
       2   
   3*pi    
-----------
       2   
128*sin (2)
$$\frac{3 \pi^{2}}{128 \sin^{2}{\left(2 \right)}}$$ 
3*pi^2/(128*sin(2)^2)
Numerical answer [src] 
0.279768688043831
0.279768688043831

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

    © Mister Exam – Calculator