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Integral of sqrt(3-2x-x^2)
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Graphing y =:
sqrt(3-2x-x^2)
Identical expressions
sqrt(three - two x-x^2)
square root of (3 minus 2x minus x squared )
square root of (three minus two x minus x squared )
√(3-2x-x^2)
sqrt(3-2x-x2)
sqrt3-2x-x2
sqrt(3-2x-x²)
sqrt(3-2x-x to the power of 2)
sqrt3-2x-x^2
sqrt(3-2x-x^2)dx
Similar expressions
sqrt(3+2x-x^2)
sqrt(3-2x+x^2)

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

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

The solution

You have entered [src]

  1                     
  /                     
 |                      
 |     ______________   
 |    /            2    
 |  \/  3 - 2*x - x   dx
 |                      
/                       
-1

$$\int\limits_{-1}^{1} \sqrt{- x^{2} - 2 x + 3}\, dx$$

Simplify

Detail solution

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

Now simplify:

$\frac{\left(x + 1\right) \sqrt{- x^{2} - 2 x + 3}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} + \frac{1}{2} \right)}$
Add the constant of integration:

$\frac{\left(x + 1\right) \sqrt{- x^{2} - 2 x + 3}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} + \frac{1}{2} \right)}+ \mathrm{constant}$

The answer is:

$\frac{\left(x + 1\right) \sqrt{- x^{2} - 2 x + 3}}{2} + 2 \operatorname{asin}{\left(\frac{x}{2} + \frac{1}{2} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                    
 |                                                                     
 |    ______________                             ______________        
 |   /            2                 /1   x\     /      2        /1   x\
 | \/  3 - 2*x - x   dx = C + 2*asin|- + -| + \/  3 - x  - 2*x *|- + -|
 |                                  \2   2/                     \2   2/
/

$${{x\,\sqrt{-x^2-2\,x+3}}\over{2}}+{{\sqrt{-x^2-2\,x+3}}\over{2}}-2 \,\arcsin \left({{-2\,x-2}\over{4}}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

pi

$$\pi$$

pi

$$\pi$$

Simplify

Numerical answer [src]

3.14159265358979

3.14159265358979

The graph

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

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

Limits of integration:

The graph:

Piecewise:

The solution