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(6y-y^2)^0.5
Solving integrals/ (6y-y^2)^0.5

Integral of (6y-y^2)^0.5 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3                 
  /                 
 |                  
 |     __________   
 |    /        2    
 |  \/  6*y - y   dy
 |                  
/                   
0
$$\int\limits_{0}^{3} \sqrt{- y^{2} + 6 y}\, dy$$ 
Integral(sqrt(6*y - y^2), (y, 0, 3))
Detail solution

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

  1. Now simplify:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                 
 |                              /     y\                            
 |    __________          9*asin|-1 + -|      ____________          
 |   /        2                 \     3/     /    2        /  3   y\
 | \/  6*y - y   dy = C + -------------- + \/  - y  + 6*y *|- - + -|
 |                              2                          \  2   2/
/
$$\int \sqrt{- y^{2} + 6 y}\, dy = C + \left(\frac{y}{2} - \frac{3}{2}\right) \sqrt{- y^{2} + 6 y} + \frac{9 \operatorname{asin}{\left(\frac{y}{3} - 1 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
9*pi
----
 4
$$\frac{9 \pi}{4}$$ 
=
= 
9*pi
----
 4
$$\frac{9 \pi}{4}$$
Упростить
Numerical answer [src] 
7.06858347057703
7.06858347057703
The graph
Integral of (6y-y^2)^0.5 dx

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

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