Find the area enclosed between the curve y=x²-1

To find the area enclosed between the curve y=x^2-1, we need to integrate the equation with respect to x over the interval where the curve is above the x-axis.

To determine the interval, we set the equation equal to zero and solve for x:

x^2-1 = 0 x^2 = 1 x = ±1

So, the interval of x-values where the curve is above the x-axis is [-1, 1].

Now, we can calculate the area by integrating the equation y=x^2-1 over the interval [-1, 1]:

Area = ∫[from -1 to 1] (x^2 - 1) dx

To evaluate the integral, we can use the power rule:

∫x^n dx = (1/(n+1)) * x^(n+1)

Applying the rule to the integral, we have:

Area = ∫[from -1 to 1] (x^2 - 1) dx = [(1/3) * x^3 - x] [from -1 to 1] = [(1/3) * 1^3 - 1] - [(1/3) * (-1)^3 - (-1)] = (1/3 - 1) - (1/3 + 1) = (1/3 - 3/3) - (1/3 + 3/3) = -2/3 - 4/3 = -6/3 = -2

The area enclosed between the curve y=x^2-1 and the x-axis is -2. However, it is not physically possible for an area to be negative, so we take the absolute value, making the area 2 units squared.