How would you approach this problem?
Find the positive value of c such that the area of the region bounded by the parabolas $y = 25x^2 - c^2$ and $y = c^2 - 25x^2$ is $\frac{8}{15}$
I'm not asking for a full walk through, but I'm just stumped as to where to start. I was thinking of going through the processes of integrating the two curves(as far as it would take me) then setting that equal to 8/15 in order to find the interval. Once the interval was calculated, I would be able to figure out how far away the two parabolas are from each other to find what the value of 'c' is.
Is this the right thought process? or is there a simpler way of finding out the value of c?
thanks in advance