Question

Question 6 The surface area obtained by rotating the curve y=e*, 75x58 about the x-axis is Your answer: 28/1+et6 +e?/1+e58-in (Ve 16+1 +68 14 + 1 +e? Tiin VI +p?te (1+e?V1+14 -e?1+e 14 + In 816 +1 +816 e 14 +1 +e? acevo e 16+1 +8 V 1+ 216 - 07/1+e 14 + Inl 14 +1+e?

hw assignment 6

Answer 1

is rotated When about x-axis, the fornit -section be seer in the below figure er Cass (60) 3 G> 2 for the strip, ds At dic? At as = Js- of te a distance of a from y-axis let's consider rectangular stop thickness de and height this strip is rotated about x-axis e it forms a Surface whose whose surface area is given by: aalto When

Schafenyl Sa ds= (d) dx -S1+(12) 2 de 3 5 QA = 27 et Ja teza de 17e2e dhe 2= 6 22 ť ed let.ee-t =) e -) A = { ar Jert at 8 dt= e²dx At, a=6, t=e x=8, t=es = A= 2T 1+t² dt Now, let t= tamo e6 »') =) A =21 1+ tanto sec²o do 1+t² = sec²o dt= sezo do At, t= eo tano = et -) 0 - tances 4t=2 tan o=e6 tar o=8 ſite! seco 2 =) O=tan (e) 12 gen Seco Same tan (66) tan o = A=27 seco seco do tan (6) tant(e) A= 25 کام الہ tant (3) 25 seco do (seco) (seco) do tan Les tance)

Now! tay (8) gec 8) &sec²o) do Let tance) tant (6) Performing integration by parts, (seco) afsezodo Ttances) I= ((5 etodo ) 3g (09) de tankes) tanke tant (e) I = [seco tano turkey (tano tanke") (seco tano) do ) (se tance) a sec =) I = sec (tant (68) tan (tant(e) sec. (tant (66) tan (tances) tani (B) seco ( seco-1) do (since, tam?o = sec28-1 tant(e) (sec'(+elt) tan (taril(89) (see's It elz) tan (tanles tant (68) secondo tante le tue tant (es) In sec(0) + tail (eo seco do tante -) 21 - Gesteld)en fines) et + [lu 1 219) turbo ) -) i= eyetek - en Satent en she see (tan(eo+ tan (tail (4) sec (tant (68) + tan (tant.

= 21 = eltelt - eltel2 thel sec bula (ezëlly Itell)) + tan(tan? (9) - In [sec(sez'( 472e)) + fauftow' (c) 2) 21 z ex litete e" Street the fratele tes]-eufdores & Setelb _eolate12 thu lweltal tee -) 212 Jertet = 1 = & Satelt - e6itel2 + enfreibti te ezt i qet Now, A = 2TI A = (271) e16 hal sales Jarede er direkten 2 12 es =\A 1 ted6ces Ite22 teule 16th te Jezi teo Option 1 t Sures is misprinted. Instead should be a telo of
Replace 6 with 7 and 12 with 14 in the final answer. I have done the same question for lim 6 to 8. Logic will be same. Although the options for the answer is misprinted