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?

Question

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?

amistre64 · Answer

the area under the curve is equal to 36

amistre64 · Answer

c is a constant here that you are trying to determine

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

if you can read thru the typos... i hope its helpful

amistre64 · Answer

something like this

anonymous · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

then substituting c for x

anonymous · Answer

why would you have to take half

amistre64 · Answer

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

amistre64 · Answer

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 :)

amistre64 · Answer

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

anonymous · Answer

oh I got it Thanks for the help!

amistre64 · Answer

youre welcome