Unformatted text preview: Math 152, Spring 2008, Review Problems for the Final Exam Your final exam is likely to have problems that do not resemble these review problems. You should also look at the review problems for the first and second exams. (1) Let R be the region in the xyplane bounded by y = x 2 4 x + 4 and y = x . (a) Find the volume of the solid obtained by rotating R about the xaxis. (b) Find the volume of the solid obtained by rotating R about the yaxis. (2) Evaluate Z x 2 1 x 2 dx and Z e x e 2 x + 4 dx . (3) Find a reduction formula for the integral Z ∞ 2 x n e 5 x dx . (4) Find a reduction formula for Z tan n xdx . (5) Find Z dx x 2 + 10 x + 34 and Z dx √ 2 x x 2 . (6) Find Z dx (1 + x 2 ) 3 and Z sin 5 x cos 2 xdx . (7) Find N such that the Trapezoidal Rule with N subintervals approximates Z 5 3 e x 2 dx with accuracy better than 0 . 0001. (8) Find Z x (ln x ) 2 dx and Z tan 1 xdx . (9) Find the surface area of the surface obtained by rotating y = √ 7 x 2 , 0 ≤ x ≤ 1 about the...
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 Spring '08
 sc
 Math, dx, Parametric equation, Euler

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