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Unformatted text preview: x for the following quantities: (a) The volume obtained by revolving R about the xaxis (b) The volume obtained by revolving R about the yaxis (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 crosssections 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 ≤ 11 √ 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 xx 2 above the interval [0,2], by completing the following steps. a) (2 pts) Write a formula for the nth 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
 AKOS
 Math, pts, 3 pts, 2 pts, 4 pts, 3pts

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