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sqrt(36-9x^2)-3
Solving integrals/ sqrt(36-9x^2)-3

Integral of sqrt(36-9x^2)-3 dx

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The solution

You have entered [src] 
  2                        
  /                        
 |                         
 |  /   ___________    \   
 |  |  /         2     |   
 |  \\/  36 - 9*x   - 3/ dx
 |                         
/                          
-2
∫−22(−9x2+36−3) dx\int\limits_{-2}^{2} \left(\sqrt{- 9 x^{2} + 36} - 3\right)\, dx 
Integral(sqrt(36 - 9*x^2) - 1*3, (x, -2, 2))
Detail solution

  1. Integrate term-by-term:

      SqrtQuadraticRule(a=36, b=0, c=-9, context=sqrt(36 - 9*x**2), symbol=x)

    1. The integral of a constant is the constant times the variable of integration:

      ∫((−1)3) dx=−3x\int \left(\left(-1\right) 3\right)\, dx = - 3 x

    The result is: x36−9x22−3x+6asin⁡(x2)\frac{x \sqrt{36 - 9 x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}

  2. Now simplify:

    3x4−x22−3x+6asin⁡(x2)\frac{3 x \sqrt{4 - x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}

  3. Add the constant of integration:

    3x4−x22−3x+6asin⁡(x2)+constant\frac{3 x \sqrt{4 - x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}+ \mathrm{constant}

The answer is:

3x4−x22−3x+6asin⁡(x2)+constant\frac{3 x \sqrt{4 - x^{2}}}{2} - 3 x + 6 \operatorname{asin}{\left(\frac{x}{2} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                                
 |                                                      ___________
 | /   ___________    \                                /         2 
 | |  /         2     |                      /x\   x*\/  36 - 9*x  
 | \\/  36 - 9*x   - 3/ dx = C - 3*x + 6*asin|-| + ----------------
 |                                           \2/          2        
/
x 36−9 x22−3 x+6 arcsin⁡(x2){{x\,\sqrt{36-9\,x^2}}\over{2}}-3\,x+6\,\arcsin \left({{x}\over{2}} \right)
Simplify
The graph
-2.0-1.5-1.0-0.52.00.00.51.01.5-1010
Plot the graph f(x)
The answer [src] 
-12 + 6*pi
6 π−126\,\pi-12 
=
= 
-12 + 6*pi
−12+6π-12 + 6 \pi
Simplify
Numerical answer [src] 
6.84955592153876
6.84955592153876
The graph
Integral of sqrt(36-9x^2)-3 dx

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

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