Mister Exam

Other calculators

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

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)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

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

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

    © Mister Exam – Calculator