Mister Exam

Other calculators

Solving integrals/ ((1÷Sin^2x)-2Cosx)dx

Integral of ((1÷Sin^2x)-2Cosx)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                        
 --                        
 2                         
  /                        
 |                         
 |  /   1              \   
 |  |------- - 2*cos(x)| dx
 |  |   2              |   
 |  \sin (x)           /   
 |                         
/                          
0
$$\int\limits_{0}^{\frac{\pi}{2}} \left(- 2 \cos{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx$$ 
Integral(1/(sin(x)^2) - 2*cos(x), (x, 0, pi/2))
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of cosine is sine:

      So, the result is:

    1. Don't know the steps in finding this integral.

      But the integral is

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                               
 |                                                
 | /   1              \                     cos(x)
 | |------- - 2*cos(x)| dx = C - 2*sin(x) - ------
 | |   2              |                     sin(x)
 | \sin (x)           /                           
 |                                                
/
$$\int \left(- 2 \cos{\left(x \right)} + \frac{1}{\sin^{2}{\left(x \right)}}\right)\, dx = C - 2 \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
oo
$$\infty$$ 
=
= 
oo
$$\infty$$ 
oo
Numerical answer [src] 
8.77994629793243e+18
8.77994629793243e+18

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

    © Mister Exam – Calculator