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  • Identical expressions

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  • absolute(sin(x))*sqrt(1+cos(x)^2)dx

  • Similar expressions

  • absolute(sin(x))*sqrt(1-cos(x)^2)
  • absolute(sinx)*sqrt(1+cosx^2)
Solving integrals/ absolute(sin(x))*sqrt(1+cos(x)^2)

Integral of absolute(sin(x))*sqrt(1+cos(x)^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                             
  /                             
 |                              
 |              _____________   
 |             /        2       
 |  |sin(x)|*\/  1 + cos (x)  dx
 |                              
/                               
0
$$\int\limits_{0}^{\pi} \sqrt{\cos^{2}{\left(x \right)} + 1} \left|{\sin{\left(x \right)}}\right|\, dx$$ 
Integral(Abs(sin(x))*sqrt(1 + cos(x)^2), (x, 0, pi))
The answer (Indefinite) [src] 
  /                                     /                            
 |                                     |                             
 |             _____________           |    _____________            
 |            /        2               |   /        2                
 | |sin(x)|*\/  1 + cos (x)  dx = C +  | \/  1 + cos (x) *|sin(x)| dx
 |                                     |                             
/                                     /
$$\int \sqrt{\cos^{2}{\left(x \right)} + 1} \left|{\sin{\left(x \right)}}\right|\, dx = C + \int \sqrt{\cos^{2}{\left(x \right)} + 1} \left|{\sin{\left(x \right)}}\right|\, dx$$
Simplify
The answer [src] 
 pi                           
  /                           
 |                            
 |     _____________          
 |    /        2              
 |  \/  1 + cos (x) *sin(x) dx
 |                            
/                             
0
$$\int\limits_{0}^{\pi} \sqrt{\cos^{2}{\left(x \right)} + 1} \sin{\left(x \right)}\, dx$$ 
=
= 
 pi                           
  /                           
 |                            
 |     _____________          
 |    /        2              
 |  \/  1 + cos (x) *sin(x) dx
 |                            
/                             
0
$$\int\limits_{0}^{\pi} \sqrt{\cos^{2}{\left(x \right)} + 1} \sin{\left(x \right)}\, dx$$ 
Integral(sqrt(1 + cos(x)^2)*sin(x), (x, 0, pi))
Numerical answer [src] 
2.29558714939264
2.29558714939264

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

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