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Unformatted text preview: x for the following quantities: (a) The volume obtained by revolving R about the x-axis (b) The volume obtained by revolving R about the y-axis (c) The volume obtained by revolving R about the line x =-2 Problem IV. (4 pts) A solid has circular base of radius 1. Find the volume of the solid if the cross-sections perpendicular to the base are isosceles right triangles with hypotenuse in the base Problem V. (4 pts) Prove the following inequality. Explain all steps in your proof: Z π/ 4 sin( x 2 ) dx ≤ 1-1 √ 2 Hint: Compare the integrand to a simpler function. Problem VI. (6 pts) Find the area A of the region under the graph y = 2 x-x 2 above the interval [0,2], by completing the following steps. a) (2 pts) Write a formula for the n-th approximating Riemann sum to the area. b) (4 pts) Evaluate and simplify the sums you obtained and ﬁnd the limit as n → ∞ ....
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- Spring '10
- Math, pts, 3 pts, 2 pts, 4 pts, 3pts