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Integral of (-1/sqrt(x))+cos(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  0                      
  /                      
 |                       
 |  /    1           \   
 |  |- ----- + cos(x)| dx
 |  |    ___         |   
 |  \  \/ x          /   
 |                       
/                        
pi                       
--                       
2                        
$$\int\limits_{\frac{\pi}{2}}^{0} \left(\cos{\left(x \right)} - \frac{1}{\sqrt{x}}\right)\, dx$$
Integral(-1/sqrt(x) + cos(x), (x, pi/2, 0))
Detail solution
  1. Integrate term-by-term:

    1. The integral of cosine is sine:

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

      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:

      So, the result is:

    The result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            
 |                                             
 | /    1           \              ___         
 | |- ----- + cos(x)| dx = C - 2*\/ x  + sin(x)
 | |    ___         |                          
 | \  \/ x          /                          
 |                                             
/                                              
$$\int \left(\cos{\left(x \right)} - \frac{1}{\sqrt{x}}\right)\, dx = C - 2 \sqrt{x} + \sin{\left(x \right)}$$
The graph
The answer [src]
       ___   ____
-1 + \/ 2 *\/ pi 
$$-1 + \sqrt{2} \sqrt{\pi}$$
=
=
       ___   ____
-1 + \/ 2 *\/ pi 
$$-1 + \sqrt{2} \sqrt{\pi}$$
-1 + sqrt(2)*sqrt(pi)
Numerical answer [src]
1.50662827379146
1.50662827379146

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