Question

The area of the surface obtained by rotating the curve x=1/4 y²−ln(y​), 1≤γ≤5 about the x-axis is ____

Answer 1

To find the area of the surface obtained by rotating the curve x=1/4 y²−ln(y), we can use the formula for finding the surface area of a surface of revolution.

Step-by-step explanation:

To find the area of the surface obtained by rotating the curve x=1/4 y²−ln(y) about the x-axis, we can use the formula for finding the surface area of a surface of revolution. The formula is: A = 2π ∫(r(x)√(1+(f'(x))^2)) dx, where r(x) is the radius of rotation and f(x) is the function being rotated. In this case, r(x) = y and f(x) = 1/4 y²−ln(y). So we have: A = 2π ∫(y√(1+(1/2 y−1)^2)) dx.