Final answer:
To find the exact area of the surface obtained by rotating the curve y = cos(18x) about the x-axis, we need to use the formula for the surface area of a solid of revolution. The formula is given by: A = 2π ∫[a,b] f(x) sqrt(1 + (f'(x))^2) dx. In this case, f(x) = cos(18x). We can plug in the values for a and b, which are 0 and 4 respectively, to find the exact area using integration.
Step-by-step explanation:
Find the exact area of the surface obtained by rotating the curve y = cos(18x) about the x-axis, where 0 ≤ x ≤ 4?
To find the exact area of the surface obtained by rotating the curve y = cos(18x) about the x-axis, we need to use the formula for the surface area of a solid of revolution. The formula is given by:
A = 2π ∫[a,b] f(x) sqrt(1 + (f'(x))^2) dx
In this case, f(x) = cos(18x). We can plug in the values for a and b, which are 0 and 4 respectively, to find the exact area using integration.