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.

Answer 1

If the area between the graph of y = x^2 - c^2 and the x-axis is 36, then
$\int\limits^c_{-c} {(x^2-c^2)} \, dx =36\\ \frac{x^3}{3}-c^2x \left \} {{c} \atop {-c}} \right. =36\\\frac{c^3}{3}-c^3+\frac{c^3}{3}-c^3=36\\\frac{-4c^3}{3}=36\\c^3=-27\\c=-3$
Therefore, the exact positive value of c is 3.