Calculus II Problems - Fall2008_Prelim1

# 4 48 points evaluate the following integrals or show

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Unformatted text preview: B in [+ß ,], and 2 is the length of each subinterval). 4) (48 points) Evaluate the following integrals or show that they diverge: a) ( B cos B .B d) ( e ÈB .B Î# b) ( ! sin# B .B \$ B .B e) ( # \$Î# ! Ð*  B Ñ NOTE: There are some formulas on the other side which may be useful. / c) ( ln B .B " B#  " f)( .B B" TRIGONOMETRIC IDENTITIES sin 2x = 2 sin x cos x cos 2x = cos2 x − sin2 x 2 sin x = 1−cos 2x 2 cos2 x = 1+cos 2x 2 cos2 x + sin2 x = 1 1 + tan2 x = sec2 x cot2 x + 1 = csc2 x DERIVATIVE FORMULAS d dx sin x = cos x d dx sin−1 x = √1 1−x2 d dx tan x = sec2 x d dx tan−1 x = 1 1+x2 d dx sec x = sec x tan x d dx sec−1 x = √1 x x2 −1 d dx cos x = − sin x d dx cos−1 x = − √11 x2 − d dx cot x = csc2 x d dx 1 cot−1 x = − 1+x2 d dx csc x = − csc x cot x d dx 1 csc−1 x = − x√x2 −1 INTEGRAL FORMULAS xn dx = xn+1 n+1 + C for n = −1 ex dx = ex + C 1 x dx = ln |x| + C sin x dx = − cos x + C cos x dx = sin x + C sec x dx = ln | sec x + tan x| + C csc x dx = − ln | csc x + cot x| + C sec2 x dx = tan x + C √1 1−x2 1 1+x2 dx = sin−1 x + C dx = tan−1 x + C...
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## This note was uploaded on 02/03/2014 for the course MATH 1120 taught by Professor Gross during the Fall '06 term at Cornell.

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