**Unformatted text preview: **x = re iθ . 9. Consider the region under the curve y = e-x and above the x-axis for 0 ≤ x < ∞ . a. Revolve it around the x-axis and ﬁnd the volume. b. Revolve it around the y-axis and ﬁnd the volume. 10. Find the arc length of the curve given by y = x 2 for 0 ≤ x ≤ √ 2. (You may ﬁnd the formula Z sec 3 θ dθ = sec θ tan θ 2 + 1 2 Z sec θ dθ useful.) 11. The mass m of a crystal in a solution grows at a rate proportional to m 2 / 3 . The original mass is 1 gram and the mass after 24 hours is 8 grams. Find the exact value of the mass as a function of time....

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- Fall '07
- Nelson
- Calculus, Integrals, Cartesian Coordinate System, Mass, Polar coordinate system