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\\ (x^3)/(3)-c^2x \left \} {{c} \atop {-c}} \right. =36\\(c^3)/(3)-c^3+(c^3)/(3)-c^3=36\\(-4c^3)/(3)=36\\c^3=-27\\c=-3`
Therefore, the exact positive value of c is 3.