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Kouba
Worksheet 13 1.) True or False. 1 d l 1 X c
a.) 1+ex X: n( +8 )+
ex
“ _ x
b.) J1+92x dx _arctan(e )+ C C.) J(1+lnx) dx = xlnx + C d.) Jxx(1+lnx) dx = xX + C 2.) Set up but do not evaluate integrals which represent the total mass of
each of the following objects. a.) A thin rod 20 cm. long has constant density of 3 gm./cm. b.) A thin rod 20 cm. long has variable density. Its density at a
point x cm. from its left end is given by x / (1 + x 2) gm./cm. c.) A hemispherical solid of radius 10 ft. has variable density. At a distance of h ft. from its flat, circular base, the density is given by
h3e'h kg./ft. 3 3.) Let f(x) be the distance from (0,0) to the point (x, y) on the graph
of y=x2. What is the average value of fon the interval [ O , V15] ? 4.) integrate. t t
a.) lmdx b.) [ff—75““ 1 l
0) l W dx d.) I xix—5 dx
‘l 5.) A "point" mass measuring 200 gm. is moving in a circular path of
radius 2 ft., completing 3 revolutions per second. What is the kinetic
energy of this moving object? (Recall : K.E. = 1/2 m v 2 .) 6.) A flat, circular plate of uniform density has a radius of 2 ft. and a
mass of 200 gm. Spinning about it axis of revolution, the plate makes 3 revolutions per second. What is the kinetic energy of this moving object
if the axis of revolution passes through a.) . its center ?
b.) a diameter ? 7.) W H20 level Find the total force due
5 9. H. to water pressure on
' one side of the
submerged,
triangular (flat) plate.
5 .
7 H. H 8.) A flat 5 ft. x 7 ft. plate is submerged in 10 ft. of water. It rests on its 5 ft. edge. Set up an integral for the total force due to water pressure
on one side of the plate if a.) it rests vertically.
b.) it rests tilted 30 0 from vertical. ...
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 Winter '07
 MAT21B

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