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Unformatted text preview: R in the plane bounded between the curves y = x and y = x 2 . (a) Find the area of R . (b) Find the volume of the solid obtained by revolving R about the xaxis. (c) Find the volume of the solid obtained by revolving R about the line x = 1. 6. True / False: (You do not need to justify your answer.) (a) Simpson’s Rule usually, but not always, gives a more accurate approximation for a deﬁnite integral than both the Midpoint Rule and the Trapezoid Rule. (b) If f ( x ) ≤ g ( x ) and ± ∞ g ( x ) dx diverges, then ± ∞ f ( x ) dx also diverges. (c) ± sin 2 x dx = 1 3 sin 3 x + C . (d) It is possible to antidiﬀerentiate every rational function in terms of ﬁnitely many familiar functions. (e) If ± ∞ a f ( x ) dx and ± ∞ a g ( x ) dx are both divergent, then ± ∞ a [ f ( x ) + g ( x )] dx is also divergent....
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 '07
 Butscher,A
 Calculus, Integrals, dx, ln x dx, dx diverges

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