1. Suppose that a and b are real numbers with a ≤ b and r and R are functions, both continuous on [a, b], with R ≥ r ≥ 0
Posted: Tue May 10, 2022 4:26 pm
1. Suppose that a and b are real numbers with a ≤ b and r and R are functions, both continuous on [a, b], with R ≥ r ≥ 0 on [a, b]. What is the volume of the solid obtained by revolving, around the x-axis, the region of the (x, y)-plane bounded by x = a, x = b, y = r(x), and y = R(x)?
2. Suppose that a and b are real numbers with 0 ≤ a ≤ b, h and H are functions, both continuous on [a, b], with H ≥ h on [a, b]. What is the volume of the solid obtained by revolving, around the y-axis, the region of the (x, y)-plane bounded by x = a, x = b, y = h(x), and y = H(x)?
2. Suppose that a and b are real numbers with 0 ≤ a ≤ b, h and H are functions, both continuous on [a, b], with H ≥ h on [a, b]. What is the volume of the solid obtained by revolving, around the y-axis, the region of the (x, y)-plane bounded by x = a, x = b, y = h(x), and y = H(x)?