Question

1. A, on a coordinate axis (1)sketch x? + (y – 5)2 = 9, (2)describe the graph, (3)the graph is revolved about the x-axis, set-up integral which will compute its VOLUME, simplify the integrand as much as possible but DO NOT DO THE INTEGRATION. B. The triangle whose vertices are (0,0), (2,8) and (2,2) is revolved around the (a)x-axis, (b)y-axis (1)find the eqs. Of the sides, (2)draw graph, (3)compute (a) and (b) C. A student on test was asked to find the volume of y = f(x) > 0, on [a,b] revolved around the y-axis and wrote CORRECTLY the integral: 275* x* sin(x®)d« what is fx)? [a,b]? Finish the computation. 2. A. Plot r = 2 sin + 1 B. Change from polar to rectangular:r = 2 sin , describe the graph. C. (1) Where do the curves r = 2 sin 0 and r = 2 cosmeet? (2) Set-up only for the problem: Find the area between these curves

Answer 1

- revolue about x-ans. we Kuono, Cvolume of solids of Revention about X-aas) It a plane area boonded by the curve y=fw), the ordinates x=b and the n-axis then volume of the solid thus generated it So my?dx = Left (fagorda (8-5² = 9-x² b 77 y = 54 19-42 since lie aboven-axis 4= 5 + Jg -12 3 rotation about n-anis V= tig-1² -3 3 an 7 (25+ (9-x2)+10 Jg=v2) du _3 347 datlon (dg - uz dn-t (n? Sunda 3 = -3 -] اور اور اور 8 0 8 jina la (2 voch te=2 Darbo la $2,2) we know each of like passing through two Point (1,4) & (M2, 42) u=x by 2851 0 (0,0) 4-4, % -% 2 - X 12-14 ou of 0 A, 061, 4, ) = (0,0) 61(44, 4,) = (2,6) x-8 = y = 4x ean of Ob olup, y) = (0,0) & B (M2, G2) = (2,2) - Y=n Y-0 8-0 - Ko 2 Ewth of AB 2-0 is a=2

voluem when revolve about x-axis, V = TY² dx- Where'Y = (4 xi-x) Volume of solaan revolve about n-ay's, (@ 2 2 I (4x)?du V= brydex filmom > lou budu- de I 8 "(16-1)= 4017 4 -) 160 b fr 3 volomei cu chen revolve about y- ani's B V- fox² dy = ༡༦ IT Idy 0 Cy) TT 46 [x3] = 9883 1- TT XS12 T vs 4432 [512-32] - 160 T revolve about y-ax's them formula Shord 6 SI (f (y))? dy form out give integral is v=x* r (4) » which is correct OWO le it is transformation them fw) = xsin x3 &' [a,b] =[447, from a fly to y = f(x) BIT

Now VT 21 utsin man wobble D 27 [cas uz huo 20 [cost - 27 (-1-1] = un cos 11 – cose] 3 s — и sy NOTE 8 f(x) kasing² & [a, b] =[T, FL since 2 is given with integral it 2 was not there then [ab] = Cour (1) Me oulous