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sqrt(12-3x^2)
Solving integrals/ sqrt(12-3x^2)

Integral of sqrt(12-3x^2) dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
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 |     ___________   
 |    /         2    
 |  \/  12 - 3*x   dx
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0
∫01−3x2+12 dx\int\limits_{0}^{1} \sqrt{- 3 x^{2} + 12}\, dx 
Integral(sqrt(12 - 3*x^2), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=12, b=0, c=-3, context=sqrt(12 - 3*x**2), symbol=x)

  1. Now simplify:

    3(x4−x2+4asin⁡(x2))2\frac{\sqrt{3} \left(x \sqrt{4 - x^{2}} + 4 \operatorname{asin}{\left(\frac{x}{2} \right)}\right)}{2}

  2. Add the constant of integration:

    3(x4−x2+4asin⁡(x2))2+constant\frac{\sqrt{3} \left(x \sqrt{4 - x^{2}} + 4 \operatorname{asin}{\left(\frac{x}{2} \right)}\right)}{2}+ \mathrm{constant}

The answer is:

3(x4−x2+4asin⁡(x2))2+constant\frac{\sqrt{3} \left(x \sqrt{4 - x^{2}} + 4 \operatorname{asin}{\left(\frac{x}{2} \right)}\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                          
 |                              ___________                  
 |    ___________              /         2                   
 |   /         2           x*\/  12 - 3*x         ___     /x\
 | \/  12 - 3*x   dx = C + ---------------- + 2*\/ 3 *asin|-|
 |                                2                       \2/
/
x 12−3 x22+2 3 arcsin⁡(x2){{x\,\sqrt{12-3\,x^2}}\over{2}}+2\,\sqrt{3}\,\arcsin \left({{x }\over{2}}\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
         ___
3   pi*\/ 3 
- + --------
2      3
2 3 π+96{{2\,\sqrt{3}\,\pi+9}\over{6}} 
=
= 
         ___
3   pi*\/ 3 
- + --------
2      3
32+3π3\frac{3}{2} + \frac{\sqrt{3} \pi}{3}
Simplify
Numerical answer [src] 
3.31379936423422
3.31379936423422
The graph
Integral of sqrt(12-3x^2) dx

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

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