Surface area of revolution practice problems
Surface area of revolution: 2π ∫ (radius) √(1 + (y′)²) dx. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Find the area of the surface obtained by rotating \( \displaystyle y = 2 x \), \( \displaystyle 0 \le x \le 3 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = \sqrt{25 - x^{2}} \), \( \displaystyle 0 \le x \le 4 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = x^{3} \), \( \displaystyle 0 \le x \le 1 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = \sqrt{x} \), \( \displaystyle 3 \le x \le 6 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = \sqrt{4 - x^{2}} \), \( \displaystyle -1 \le x \le 0 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = x \), \( \displaystyle 0 \le x \le 1 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = \sqrt{x} \), \( \displaystyle 0 \le x \le 2 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = \sqrt{4 - x^{2}} \), \( \displaystyle -1 \le x \le 1 \), about the \( \displaystyle x \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = x^{2} \), \( \displaystyle 0 \le x \le 1 \), about the \( \displaystyle y \)-axis.
Find the area of the surface obtained by rotating \( \displaystyle y = 3 x \), \( \displaystyle 0 \le x \le 2 \), about the \( \displaystyle x \)-axis.