Final answer:
To find the exact area of the surface obtained by rotating the curve y = 1 ex about the x-axis for 0 ≤ x ≤ 7, you can use the formula for the surface area of a solid of revolution and evaluate the integral.
Step-by-step explanation:
To find the exact area of the surface obtained by rotating the curve y = 1 ex about the x-axis for 0 ≤ x ≤ 7, we can use the formula for the surface area of a solid of revolution. The formula is given by:
A = 2π ∫[a, b] f(x) √(1 + (f'(x))²) dx
In this case, f(x) = 1 ex and the limits of integration are a = 0 and b = 7. We can substitute these values into the formula and evaluate the integral to find the exact area.