Mister Exam

Other calculators

sqrt(6x-x^2)
Solving integrals/ sqrt(6x-x^2)

Integral of sqrt(6x-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  6*x - x   dx
 |                  
/                   
0
$$\int\limits_{0}^{1} \sqrt{- x^{2} + 6 x}\, dx$$ 
Integral(sqrt(6*x - x^2), (x, 0, 1))
Detail solution

    SqrtQuadraticRule(a=0, b=6, c=-1, context=sqrt(-x**2 + 6*x), symbol=x)

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                 
 |                              /     x\                            
 |    __________          9*asin|-1 + -|      ____________          
 |   /        2                 \     3/     /    2        /  3   x\
 | \/  6*x - x   dx = C + -------------- + \/  - x  + 6*x *|- - + -|
 |                              2                          \  2   2/
/
$${{x\,\sqrt{6\,x-x^2}}\over{2}}-{{3\,\sqrt{6\,x-x^2}}\over{2}}-{{9\, \arcsin \left({{6-2\,x}\over{6}}\right)}\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    ___   9*asin(2/3)   9*pi
- \/ 5  - ----------- + ----
               2         4
$${{9\,\pi}\over{4}}-{{9\,\arcsin \left({{2}\over{3}}\right)+2\, \sqrt{5}}\over{2}}$$ 
=
= 
    ___   9*asin(2/3)   9*pi
- \/ 5  - ----------- + ----
               2         4
$$- \frac{9 \operatorname{asin}{\left(\frac{2}{3} \right)}}{2} - \sqrt{5} + \frac{9 \pi}{4}$$
Упростить
Numerical answer [src] 
1.5487410400559
1.5487410400559
The graph
Integral of sqrt(6x-x^2) dx

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

    © Mister Exam – Calculator