Question

find the area of the region that is bounded by the curve f(x)=x2−4 and the line g(x)=x 2 over the interval [−3,−1]. enter an exact answer.

Answer 1

The area bounded by the curve f(x)=x2−4 and the line g(x)=x 2 over the interval [-3,−1] is 0.

Step-by-step explanation:

To find the area of the region bounded by the curve f(x) = x^2 - 4 and the line g(x) = x^2 over the interval [-3, -1], we need to calculate the definite integral of the difference between the two curves within that interval. Let's find the points of intersection first:

Finding the intersection points:

1. Set f(x) = g(x):
2. Subtract x^2 from both sides:
3. There are no solutions to the equation, meaning the two curves do not intersect. Therefore, the area bounded by these curves over the interval [-3, -1] is 0.