Exam 2 Solutions 2011

10 points find sec2 1d tan c dx x 9 x2 solution

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Unformatted text preview: ted) tan2 (θ) = sec2 (θ) − 1 so tan2 (θ)dθ = 6. (10 points) Find sec2 (θ) − 1dθ = tan(θ) − θ + C dx √ . x 9 − x2 Solution: (corrected) 3 9 x 2 Θ x Referring to the triangle above, let x/3 = cos(θ) and √ 9 − x2 /3 = sin(θ) so x = 3 cos(θ) dx = −3 sin(θ) dθ 9 − x2 = 3 sin(θ) −3 sin(θ) dθ 3 cos(θ)3 sin(θ) dθ −1 = 3 cos(θ) −1 = sec(θ)dθ 3 −1 = ln(|sec(θ) + tan(θ)|) + C 3 dx √ = x 9 − x2 Referring again to the figure one can see that, written in terms of its original variable, x, the integral is √ 9 − x2 −1 3 ln + +C 3 x x 7. (10 points) Find 4x2 + 25 dx. Solution: Page 3 4x 2 25 2x Θ 5 √ Referring to the triangle above, let 2x/5 = tan(θ) and ( 4x2 + 25)/5 = sec(θ) so 5 tan(θ) 2 5 dx = se...
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This document was uploaded on 03/05/2014 for the course MAT 193 at CSU Dominguez Hills.

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