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Integral of d{x}:
Integral of csc^2xdx
Integral of sqrt(12-3x^2)
Integral of 8-2x^2
Integral of (x^2+7x-5)cos2x
Identical expressions
sqrt(twelve -3x^ two)
square root of (12 minus 3x squared )
square root of (twelve minus 3x to the power of two)
√(12-3x^2)
sqrt(12-3x2)
sqrt12-3x2
sqrt(12-3x²)
sqrt(12-3x to the power of 2)
sqrt12-3x^2
sqrt(12-3x^2)dx
Similar expressions
sqrt(12+3x^2)

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

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

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |     ___________   
 |    /         2    
 |  \/  12 - 3*x   dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \sqrt{- 3 x^{2} + 12}\, dx$$

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)

Now simplify:

$\frac{\sqrt{3} \left(x \sqrt{4 - x^{2}} + 4 \operatorname{asin}{\left(\frac{x}{2} \right)}\right)}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                          
 |                              ___________                  
 |    ___________              /         2                   
 |   /         2           x*\/  12 - 3*x         ___     /x\
 | \/  12 - 3*x   dx = C + ---------------- + 2*\/ 3 *asin|-|
 |                                2                       \2/
/

$${{x\,\sqrt{12-3\,x^2}}\over{2}}+2\,\sqrt{3}\,\arcsin \left({{x }\over{2}}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

         ___
3   pi*\/ 3 
- + --------
2      3

$${{2\,\sqrt{3}\,\pi+9}\over{6}}$$

         ___
3   pi*\/ 3 
- + --------
2      3

$$\frac{3}{2} + \frac{\sqrt{3} \pi}{3}$$

Simplify

Numerical answer [src]

3.31379936423422

3.31379936423422

The graph

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution