x2_practice_sols

x2_practice_sols - Exam 2 Review Problems Solutions Math...

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Unformatted text preview: Exam 2 Review Problems Solutions Math 175 - Fall 2009 NOTE: These are not unique solutions. In many problems a different substitution or different parts could work equally well. 1. integraldisplay e √ x √ x dx (a) Substitution (b) u = √ x du = 1 2 √ x dx (c) integraldisplay e √ x √ x dx = 2 integraldisplay e u du 2. integraldisplay x 2 √ 1- x 2 dx (a) Substitution (b) x = sin θ dx = cos θdθ x 2 = sin 2 θ √ 1- x 2 = cos θ (c) integraldisplay x 2 √ 1- x 2 dx = integraldisplay sin 2 θ cos θ cos θ dθ = integraldisplay sin 2 θdθ 1 3. integraldisplay x x + 10 dx (a) Partial fractions (b) x x + 10 = 1- 10 x + 10 (long division) (c) No other decomposition necessary. 4. integraldisplay cos x 1 + sin x dx (a) Substitution (b) u = sin x du = cos xdx (c) integraldisplay cos x 1 + sin x dx = integraldisplay 1 1 + u du 5. integraldisplay tan 7 x sec 3 xdx (a) Substitution (b) u = sec x du = sec x tan xdx tan x = √ u 2- 1 (c) integraldisplay tan 7 x sec 3 xdx = integraldisplay...
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This note was uploaded on 10/11/2011 for the course MATH 175 taught by Professor Staff during the Fall '08 term at Boise State.

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x2_practice_sols - Exam 2 Review Problems Solutions Math...

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