# Ind a horizontal line y=k that divides the area* QUESTION*

1. Jan 22, 2010

### SAT2400

ind a horizontal line y=k that divides the area*URGENT QUESTION*

1. The problem statement, all variables and given/known data
Find a horizontal line y=k that divides the area between y=x^2 and y=9into two equal parts.

2. Relevant equations
integral b,a, ( f(x) -g(x) ) dx

3. The attempt at a solution

half of the total area: 18
Integral(b,a) (k -x^2) dx = 18
Integral(b,a) (9-k) dx = 18

Please explain how to solve this !! T_T

2. Jan 22, 2010

### Altabeh

Re: ind a horizontal line y=k that divides the area*URGENT QUESTION*

Where does y=k intercept x^2? There is a couple of solutions; set 'em as the limits of the integral $$\int(9-x^2)dx=18$$. This is a simple cubic equation that has certainly one real solution. (To solve it use Cardano's method and http://www.trans4mind.com/personal_development/mathematics/polynomials/cardanoMethodExamples.htm"you can find the solved examples of how to do it.)

AB

Last edited by a moderator: Apr 24, 2017
3. Jan 22, 2010

### SAT2400

Re: ind a horizontal line y=k that divides the area*URGENT QUESTION*

Can you explain more in detail?

why do you do integral(b,a) (9- x^2) dx = 18?? isn't it 36?

y=9 is the top part

y=k will be the middle part of two areas(each 18)

y=x^2 is the bottom part..?

4. Jan 22, 2010

### Altabeh

Re: ind a horizontal line y=k that divides the area*URGENT QUESTION*

Just graph the function y=x^2 and see where y=9 intercepts it. The area surrounded by x^2and y=9 is 36; so the half of it will be encircled by y=k which intercepts x^2 at $$\pm \sqrt{k}$$.

And one typo: I must have typed $$\int(k-x^2)dx=18$$. (Sorry for inconvenience)

AB

5. Jan 22, 2010

### SAT2400

Re: ind a horizontal line y=k that divides the area*URGENT QUESTION*

how do i find the value of K??!?~

(-unknown x , k) and (unknown x , k) will be the interceptions btwn y=k and y=x^2

But/
still confused :(

6. Jan 22, 2010

### Altabeh

Re: ind a horizontal line y=k that divides the area*URGENT QUESTION*

Is solving $$\int^{+\sqrt{k}}_{-\sqrt{k}}(k-x^2)dx=18$$ the problem you have?

Here we go: $$\int^{+\sqrt{k}}_{-\sqrt{k}}(k-x^2)dx=|kx-\frac{1}{3}x^3|^{x=+\sqrt{k}}_{x=-\sqrt{k}}=|2k^{3/2}-\frac{2}{3}k^{3/2}|=18$$. Now continuing this is your job.

AB