Find the area of the region enclosed by the curves $y=x^{2}-4$ and $y=5$.
The area of the region enclosed by the curves is (Type a simplified fraction.)
Answer
Final Answer: The area of the region enclosed by the curves \(y=x^{2}-4\) and \(y=5\) is \(\boxed{36}\).
Step 1 ：Set the two functions equal to each other to find the points of intersection: \(x^{2}-4 = 5\).
Step 2 ：Solve for x to get the solutions: \(x = -3, 3\).
Step 3 ：The area enclosed by the curves is the integral of the absolute difference between the two functions over the interval defined by the points of intersection.
Step 4 ：Evaluate the integral to find the area: \(\int_{-3}^{3} |5 - (x^{2}-4)| dx = 36\).
Step 5 ：Final Answer: The area of the region enclosed by the curves \(y=x^{2}-4\) and \(y=5\) is \(\boxed{36}\).
