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sqrt(9-3x^2)
Solving integrals/ sqrt(9-3x^2)

Integral of sqrt(9-3x^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  9 - 3*x   dx
 |                  
/                   
0
∫01−3x2+9 dx\int\limits_{0}^{1} \sqrt{- 3 x^{2} + 9}\, dx 
Integral(sqrt(9 - 3*x^2), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=9, b=0, c=-3, context=sqrt(9 - 3*x**2), symbol=x)

  1. Now simplify:

    3(x3−x2+3asin⁡(3x3))2\frac{\sqrt{3} \left(x \sqrt{3 - x^{2}} + 3 \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)}\right)}{2}

  2. Add the constant of integration:

    3(x3−x2+3asin⁡(3x3))2+constant\frac{\sqrt{3} \left(x \sqrt{3 - x^{2}} + 3 \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)}\right)}{2}+ \mathrm{constant}

The answer is:

3(x3−x2+3asin⁡(3x3))2+constant\frac{\sqrt{3} \left(x \sqrt{3 - x^{2}} + 3 \operatorname{asin}{\left(\frac{\sqrt{3} x}{3} \right)}\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                     /    ___\
 |                             __________       ___     |x*\/ 3 |
 |    __________              /        2    3*\/ 3 *asin|-------|
 |   /        2           x*\/  9 - 3*x                 \   3   /
 | \/  9 - 3*x   dx = C + --------------- + ---------------------
 |                               2                    2          
/
332 arcsin⁡(x3)2+x 9−3 x22{{3^{{{3}\over{2}}}\,\arcsin \left({{x}\over{\sqrt{3}}}\right) }\over{2}}+{{x\,\sqrt{9-3\,x^2}}\over{2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
                    /  ___\
            ___     |\/ 3 |
  ___   3*\/ 3 *asin|-----|
\/ 6                \  3  /
----- + -------------------
  2              2
332 arcsin⁡(13)+62{{3^{{{3}\over{2}}}\,\arcsin \left({{1}\over{\sqrt{3}}}\right)+ \sqrt{6}}\over{2}} 
=
= 
                    /  ___\
            ___     |\/ 3 |
  ___   3*\/ 3 *asin|-----|
\/ 6                \  3  /
----- + -------------------
  2              2
62+33asin⁡(33)2\frac{\sqrt{6}}{2} + \frac{3 \sqrt{3} \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}}{2}
Simplify
Numerical answer [src] 
2.82380806105879
2.82380806105879
The graph
Integral of sqrt(9-3x^2) dx

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

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