## anonymous 5 years ago Find the exact positive value of c if the area between the graph of y=x^2-c^2 and the x -axis is 36. Does that mean x=36? but then how do i solve for c?

1. amistre64

the area under the curve is equal to 36

2. amistre64

c is a constant here that you are trying to determine

3. amistre64

in other words; what is the integral of y = x^2 + C such that it equals 36

4. amistre64

youd need to find the solution for: 108 = x (x+sqrt(3C)) (x-sqrt(3C))

5. amistre64

or simply put..... since C = c^2 108 = x (x - csqrt(3))(x + csqrt(c))

6. amistre64

7. amistre64

something like this

8. anonymous

i came out with the answer of 3 by$\int\limits_{c}^{-c}x^2-c^2$

9. anonymous

taking the antiderivative and getting x^3/3-c^2x

10. amistre64

make sure you integrate half of that area then multiply it by 2 to check yourself

11. anonymous

then substituting c for x

12. anonymous

why would you have to take half

13. amistre64

do we want the interval and the value of "c" in the equation to be the same?

14. amistre64

because the graph of y = x^2 -C is centered on the y axis; and if you take the area of that, you get "zero' regardless of where you put it :)

15. amistre64

both sides cancel each other out.... just a hazard of the trade really

16. anonymous

oh I got it Thanks for the help!

17. amistre64

youre welcome