Final answer:
The volume of the solid formed by revolving the curve y = e⁵ʱ about the x-axis can be calculated using the disk method, integrating π[y(x)]² with respect to x from the lower to upper bounds of the region. However, without the specific limits of integration, we cannot provide a numerical answer.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the curve y = e⁵ʱ about the x-axis, we can use the disk method. The volume V of the solid formed by revolving a region around the x-axis from x=a to x=b is given by the integral:
V = π ∫ᵒ=ᵃ² ᵗᵗᵆʸᵖʰᵒ⁴ᵒ ᵅˢ(
However, since the question does not provide the limits of integration (a and b), we cannot calculate a numerical answer. Additionally, the formula given in the reference for the volume of a cylinder, V = πr²h, is not directly applicable. The reference to the sphere's volume and surface area is also not pertinent to solving this problem. To calculate the actual volume of the solid using the disk method, one would need the specific boundaries of integration for the given function.