Find the positive value of c such that the area of the region bounded by the parabolas y = 9x^2 - c^2 and y = c^2 - 9x^2 is 24.

I would like a hint please, not the answer.

Question

Find the positive value of c such that the area of the region bounded by the parabolas y = 9x^2 - c^2 and y = c^2 - 9x^2 is 24.

I would like a hint please, not the answer.

turingtest · Answer

first: where do these two graphs intersect in terms of c ?

turingtest · Answer

is that tip okay, or...?

anonymous · Answer

Ok let me find that out.

anonymous · Answer

@TuringTest 
The intersection point is x = c/3.

turingtest · Answer

yeah, but don't forget +/- 
so what are our bounds?

anonymous · Answer

The bounds are -c/3 to +c/3. @TuringTest

turingtest · Answer

yes, so what have you got for a setup so far?

anonymous · Answer

OK. I get it now. We are going to make the definite integral of -c/3 to +c/3 of...

But how do you know which one is upper function and which one is lower?????

anonymous · Answer

I know that we are going to do this:

Area = definite integral from -c/3 to +c/3 of..

anonymous · Answer

OK I know

turingtest · Answer

well each one is just the graph of 9x^2 shifted up or down by c^2 so...

anonymous · Answer

For there to be two intersection points in the first place, c^2 - 9x^2 has to be the upper function

anonymous · Answer

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