Question

Chapter 8, Section 8.2, Question 083 Rotate the bell-shaped curve y = e 22 10 shown in the figure below around the y-axis, forming a hill-shaped solid of revolution. By slicing horizontally, find the volume of this hill. y=e -221 2/10 pere Enter the exact answer. 方程编辑器 Common 12 Matrix EP a b ab ah ag sin(a) sec(a) sina) cos(a) csc(a) cosa tan(a) cota tana a li { faz gas wa a U Total Volume =

Answer 1

Foro region bounded by uy the wore xefly) and y-asis betures ac y=C and g=d, dotated about y-axis, volume (V) = π d - 110 Griver, y = e - 2 V2 => ny_-x² 7 + (- 10 (ny) The graph is as • follows, 10 1 12 +1-10 (ny) = x -4-10lny) 20 Joking the the part of the purse (pantin Istquodecant) & restoting about y-cois gues us the desired volume, [think!] the coure is inbetween y=0 & y = 1 [(-10 my} ] ² dy . V- T V- T [-10 (my] dy -- 1017 [-y + y lnglo ---1011 (-1+ 6(1) +0 - O(lm (0)] 108 [-1] TOIT - 02/10 yié - The wolume of the bill obtained on grabatung the custuse g-ams is IV = 1017 units about

SUMMARY:

The volume of the "hill" is 10Pi unit³.