Calculus II Problems - Fall2008_Prelim1

4 48 points evaluate the following integrals or show

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 02/03/2014 for the course MATH 1120 taught by Professor Gross during the Fall '06 term at Cornell.

Ask a homework question - tutors are online