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Solving integrals/ sinxdx/sqrtcosx

Integral of sinxdx/sqrtcosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let .

    Then let and substitute :

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

      1. The integral of a constant is the constant times the variable of integration:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                                 
 |   sin(x)                ________
 | ---------- dx = C - 2*\/ cos(x) 
 |   ________                      
 | \/ cos(x)                       
 |                                 
/
$$\int \frac{\sin{\left(x \right)}}{\sqrt{\cos{\left(x \right)}}}\, dx = C - 2 \sqrt{\cos{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ________
2 - 2*\/ cos(1)
$$2 - 2 \sqrt{\cos{\left(1 \right)}}$$ 
=
= 
        ________
2 - 2*\/ cos(1)
$$2 - 2 \sqrt{\cos{\left(1 \right)}}$$ 
2 - 2*sqrt(cos(1))
Numerical answer [src] 
0.529894825710569
0.529894825710569

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

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