anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
the area under the curve is equal to 36
amistre64
  • amistre64
c is a constant here that you are trying to determine
amistre64
  • amistre64
in other words; what is the integral of y = x^2 + C such that it equals 36

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amistre64
  • amistre64
youd need to find the solution for: 108 = x (x+sqrt(3C)) (x-sqrt(3C))
amistre64
  • amistre64
or simply put..... since C = c^2 108 = x (x - csqrt(3))(x + csqrt(c))
amistre64
  • amistre64
if you can read thru the typos... i hope its helpful
amistre64
  • amistre64
something like this
1 Attachment
anonymous
  • anonymous
i came out with the answer of 3 by\[\int\limits_{c}^{-c}x^2-c^2\]
anonymous
  • anonymous
taking the antiderivative and getting x^3/3-c^2x
amistre64
  • amistre64
make sure you integrate half of that area then multiply it by 2 to check yourself
anonymous
  • anonymous
then substituting c for x
anonymous
  • anonymous
why would you have to take half
amistre64
  • amistre64
do we want the interval and the value of "c" in the equation to be the same?
amistre64
  • 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 :)
amistre64
  • amistre64
both sides cancel each other out.... just a hazard of the trade really
anonymous
  • anonymous
oh I got it Thanks for the help!
amistre64
  • amistre64
youre welcome

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