Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

278 Multiple and Line Integrals [Ch. 7
2301. \ where C 2 . i . 2 is the first turn of the screw-line
% ~T~ y i *
(*
# = acos/ f y = as\nt, z = bt.
2302.
J t/"2# 2
-I- z 2
ds y where C is the circle x 2
+ y 2
+z 2 = a 2
c
x=y.
2303*. Find the area of the lateral surface of the parabolic
o
cylinder y = x 2
bounded by the planes z = 0, x~0, 2 = x, = // 6.
2304. Find the arc length of the conic screw-line C x ae 1
y = ae* sin /, z = ae l
2
,
cos?,
from the point 0(0, 0, 0) to the point A (a, 0, a).
2305. Determine the mass of the contour of the ellipse
yi
2- + -T2- = l, if the linear density ot it at each point M (x, y) is
equal to \y\.
2306. Find the mass of the first turn of the screw-line A; = a cos/,
y = asmt, zbt, if the density at each point is equal to the
radius vector of this point.
2307. Determine the coordinates of the centre of gravity of
a half-arc of the cycloid
x = a(t sin /), y = a(\ cost) [0