Answer:
The area enclosed by two curves can be found by subtracting the area between one curve and the x-axis from the area between the other curve and the x-axis.
Let's call the x-value where the two curves intersect as X. At X, both y values are equal to 0. Hence, the equation for X is
-x^2 + c = x^2 - c
Solving for x, we get
2x^2 = 2c
x^2 = c
The area between y = -x^2 + c and the x-axis is equal to the area between y = x^2 - c and the x-axis, so the total area is double that, or 2c.
Setting 2c equal to 56, we have:
2c = 56
c = 28
So the value of c for which the area enclosed by the curves y = −x^2 + c and y = x^2 − c is equal to 56 is 28.