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sqrt(3-2x-x^2)
Solving integrals/ sqrt(3-2x-x^2)

Integral of sqrt(3-2x-x^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                     
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 |  \/  3 - 2*x - x   dx
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-1
∫−11−x2−2x+3 dx\int\limits_{-1}^{1} \sqrt{- x^{2} - 2 x + 3}\, dx
Simplify
Detail solution

    SqrtQuadraticRule(a=3, b=-2, c=-1, context=sqrt(-x**2 - 2*x + 3), symbol=x)

  1. Now simplify:

    (x+1)−x2−2x+32+2asin⁡(x2+12)\frac{\left(x + 1\right) \sqrt{- x^{2} - 2 x + 3}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} + \frac{1}{2} \right)}

  2. Add the constant of integration:

    (x+1)−x2−2x+32+2asin⁡(x2+12)+constant\frac{\left(x + 1\right) \sqrt{- x^{2} - 2 x + 3}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} + \frac{1}{2} \right)}+ \mathrm{constant}

The answer is:

(x+1)−x2−2x+32+2asin⁡(x2+12)+constant\frac{\left(x + 1\right) \sqrt{- x^{2} - 2 x + 3}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} + \frac{1}{2} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                    
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 |    ______________                             ______________        
 |   /            2                 /1   x\     /      2        /1   x\
 | \/  3 - 2*x - x   dx = C + 2*asin|- + -| + \/  3 - x  - 2*x *|- + -|
 |                                  \2   2/                     \2   2/
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x −x2−2 x+32+−x2−2 x+32−2 arcsin⁡(−2 x−24){{x\,\sqrt{-x^2-2\,x+3}}\over{2}}+{{\sqrt{-x^2-2\,x+3}}\over{2}}-2 \,\arcsin \left({{-2\,x-2}\over{4}}\right)
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.805
Plot the graph f(x)
The answer [src] 
pi
π\pi 
=
= 
pi
π\pi
Simplify
Numerical answer [src] 
3.14159265358979
3.14159265358979
The graph
Integral of sqrt(3-2x-x^2) dx

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

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