Question

Determine the area bound by the following functions and double

check the answers:
y = 4x²+1, y + 1-x/4, y=1/x

Answer 1

To determine the area bound by the functions y = 4x²+1, y + 1-x/4, and y = 1/x, find the intersection points of these three functions and calculate the area between them using definite integration.

Step-by-step explanation:

To determine the area bound by the functions y = 4x²+1, y + 1-x/4, and y = 1/x, we need to find the intersection points of these three functions and calculate the area between them.

To find the intersection points, we set the functions equal to each other and solve for x.

The intersection points are x = 0, x ≈ -0.239, and x ≈ 0.791.

We can then integrate each function within the bounds of these intersection points to find the area between them.

Using the definite integral, we can calculate the area bound by the functions.