MATH118MS05N

# MATH118MS05N - a Sketch the curves of r = √ 2 sin θ and...

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MATH 118, Calculus 2, Midterm, June 6th, 2005 Note: Questions not relevant to this year’s test have been omitted. 1: Integration. Solve the following integrals: a) R tan 2 x sec 4 x dx b) R - 2 x 2 + 12 x - 10 dx c) R x +2 ( x +3)( x - 2) dx d) R x 2 sin x dx e) R 1 - 1 x (1 - x 2 ) 2 dx f) R x arctan x dx 2: For the following two questions, leave your answer in fraction form (eg 93 8 ) a) Use the trapezodial rule with n = 4 to approximate the area of the region bounded by y = - 10( x - 1) 2 + 10 and the x -axis. b) Use Simpson’s rule with n = 4 to approximate the area of the region given in a). 4: Polar equations
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Unformatted text preview: a) Sketch the curves of r = √ 2 sin θ and r = q sin(2 θ ) and shade the region bounded by both curves. b) Find the slope of r = q sin(2 θ ) at the point θ = π/ 4. ANSWERS 1) a) tan 3 x 3 + tan 5 x 5 + C b) 2 √ 2 arcsin x-3 2 + √ 2 2 ( x-3) q 4-( x-3) 2 + C c) 1 5 ln | x + 3 | + 4 5 ln | x-2 | + C d)-x 2 cos x + 2 x sin x + 2 cos x + C e) The improper integral diverges. f) x 2 2 arctan x-x 2 + arctan x + C 2) a) 25 2 b) 40 3 4) b) -1 1...
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