quiz (159)

quiz (159) - PRINT Your Name Quiz 3 September 2 2011...

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PRINT Your Name: Quiz 3 — September 2, 2011 – Section 8 – 11:15 – 12:05 Remove everything from your desk except a pencil or pen. Circle your answer. Show your work. Your work should be correct and coherent. CHECK your answer. The quiz is worth 5 points. Find i x 2 + 2 xdx . Answer: We complete the square: x 2 + 2 x = ( x 2 + 2 x + 1) - 1 = ( x + 1) 2 - 1. Let x + 1 = sec θ . It follows that ( x + 1) 2 - 1 = tan 2 θ and dx = sec θ tan θdθ . The original problem is equal to I tan 2 θ sec θdθ. We use integration by parts. Let u = tan θ and dv = sec θ tan θdθ . It follows that du = sec 2 θdθ and v = sec θ . So I tan 2 θ sec θdθ = sec θ tan θ - I sec 3 θdθ = sec θ tan θ - I (tan 2 θ + 1) sec θdθ = sec θ tan θ - I sec θdθ - I tan 2 θ sec θdθ. Add i tan 2 θ sec θdθ to both sides to see that 2 I tan 2 θ sec θdθ = sec θ tan θ - I sec θdθ. So I r x 2 + 2 xdx = I tan 2 θ sec θdθ = (1 / 2) b sec θ tan θ - I sec θdθ B = (1 / 2) [sec θ tan θ - ln | sec θ + tan θ | ] + C = (1 / 2) ± ( x + 1) r x 2 + 2 x - ln

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quiz (159) - PRINT Your Name Quiz 3 September 2 2011...

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