M408C - HW 11

# M408C - HW 11 - d ±ind the value oF the integral 1(20...

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P ROBLEMS H W 11 6.2 P 362 45(use Riemann sum), 50, 51, 53, 57, 58, 60 7.2 P 402 33, 39, 65, 71, 73, 75, 79, 81, 83 7.3 P 409 25, 29, 31, 33, 61, 63 7.4 P 419 3, 7, 27, 29, 59, 63, 69, 71, 73, 75, 77 F INAL P RACTICE Q UIZ S AMPLE 1) A volume sits above the fgure in the xy -plane bounded by the parabola x = 1 y 2 For 0 x 1. Each x cross section is a halF-circle, with diameter touching the extreme ends oF the parabola.What is the volume? a) Sketch the region in the xy plane. b) What is the area oF a cross-section at x ? c) Write an integral For the volume
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Unformatted text preview: d) ±ind the value oF the integral. 1)(20 points) Find the area bounded by the curves y = sin x , y = cos x , 0 ≤ x ≤ π 2 . 2)(40 points) Find the integrals: π 4 sec 2 x tan 2 x dx sin(ln x ) x dx 3)(20 points) Let f ( x ) = xe − x on [0 , 2]. a) Diferentiate and simpli±y b) Find all critical numbers. c) Find absolute extremes. 4)(10 points) Let f ( x ) = ln x x 2 . Find all asymptotes. 5)(10 points) Find sinh x cosh x dx...
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