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sqrt(8-2x-x^2)
Solving integrals/ sqrt(8-2x-x^2)

Integral of sqrt(8-2x-x^2) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1                     
  /                     
 |                      
 |     ______________   
 |    /            2    
 |  \/  8 - 2*x - x   dx
 |                      
/                       
0
$$\int\limits_{0}^{1} \sqrt{- x^{2} - 2 x + 8}\, dx$$ 
Integral(sqrt(8 - 2*x - x^2), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=8, b=-2, c=-1, context=sqrt(-x**2 - 2*x + 8), symbol=x)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                    
 |                                  /1   x\                            
 |    ______________          9*asin|- + -|      ______________        
 |   /            2                 \3   3/     /      2        /1   x\
 | \/  8 - 2*x - x   dx = C + ------------- + \/  8 - x  - 2*x *|- + -|
 |                                  2                           \2   2/
/
$${{x\,\sqrt{-x^2-2\,x+8}}\over{2}}+{{\sqrt{-x^2-2\,x+8}}\over{2}}-{{ 9\,\arcsin \left({{-2\,x-2}\over{6}}\right)}\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___     ___   9*asin(1/3)   9*asin(2/3)
\/ 5  - \/ 2  - ----------- + -----------
                     2             2
$${{9\,\arcsin \left({{2}\over{3}}\right)+2\,\sqrt{5}}\over{2}}-{{9\, \arcsin \left({{1}\over{3}}\right)+2^{{{3}\over{2}}}}\over{2}}$$ 
=
= 
  ___     ___   9*asin(1/3)   9*asin(2/3)
\/ 5  - \/ 2  - ----------- + -----------
                     2             2
$$- \frac{9 \operatorname{asin}{\left(\frac{1}{3} \right)}}{2} - \sqrt{2} + \sqrt{5} + \frac{9 \operatorname{asin}{\left(\frac{2}{3} \right)}}{2}$$
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Numerical answer [src] 
2.57636277560449
2.57636277560449
The graph
Integral of sqrt(8-2x-x^2) dx

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

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