Question

(1 point) The region W is the cone shown below. The angle at the vertex is 1/2, and the top is flat and at a height of 4. Write the limits of integration for w DV in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry): b = (a) Cartesian: With a = c= er Volume = Sa Se .d = , and f = (b) Cylindrical: With a = he ,d= , and f = c= e= Volume = Sa So Se (c) Spherical: With a = c= er Volume = Sa So Se ,b= ,d= , and f = ddd

Answer 1

# Geren that the righ circulen Cone has angle at verter 20 = 1/2 and height 4 So ontly 3) Equation of cone Ceļty2 )(050)? .?.Çchce? = 0 - al+y647 - 22:20 - x² + y²_2²=0 f = n²y? 2² :: 2² = x² + y 2 iz= valtija Putting 2=4 & projecting the upper curcules region to xy plane aeget n²t 92=4² olacy, osy a Vibona T 3040) ... [fov - I lidz dydre where a = 0,b= 14), e=0); da mozet, e-l) 9-112793) b! In cylndrical co-ordzhater gerecoso y = fesmo.5=%. so z² = x?ty2 = z²r? ; 2=8, 8002228 - And re=re?ty2 = VT6 ay so ore 24., 050329 ( 0 *. Jis du = $911fa diz da do {=(r=x7 cs scanned wă & dy Choreca=0gb-29, C=0,-4, e-O, fari

in Spherical Co-ordinates ?-. a = f sèop coso, yopsing suso2-.coso ni+y-z? = m+42+72-a2? - paz? -0 oss V272 .. but height = 4 so z=4 A P= 132 = 422. so. Os85405 ;... o Eg the angle areeene z cruise so M.OSO=1/2. -schce a² + y ² = 7² so x² 8 schis ») L = yesind. So 9 = Sch"153) - Sch) (4) Escal G ap so 0345Ty - Sig Sau = $'Spiseo). df.48.de - a c e cilere a=0, b= Ty, =0,2 = /2 12-o, f=462. f = fing - p²eos?s. f = -fcos26 Scanned with CamScanner