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Unformatted text preview: t evaluate
the integral. ■ x œπ
„ 1, x
x x 25. ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ 4 to estimate the volume
obtained by rotating about the yaxis the region under the curve
y tan x, 0 x
4. First Exam — January 28, 2010 Page 8 of 11 28. If the region shown in the ﬁgure is rotated about the yaxis to form a solid, use the Midpoint Rule with n 1 5 to estimate the (8 points) Consider the region between the curve and the xaxis in the ﬁgure below:
volume of the solid. 1 , x 0, x 2 x y y 3 , ■ 27. Use the Midpoint Rule with n od of cylindrical shells to ﬁnd the volume genregion bounded ath 42, Winter about the
M by the given curves 2010
ion and a typical shell.
, ■ y x2 ■ ■ 4x 5
4 7 ■ ■ 3
■ ■ ■ ■ ■ 2 me of the solid obtained by rotating about the
bounded by y sx and y x 2. Find V both
cylindrical shells. In both cases draw a diaour method. 1
0 2 1 3 4 5 6 7 8 9 10 11 12 x od of cylindrical shells to ﬁnd the volume of
29–32
Each integral represents the volume of a solid. Describe
(a) by the region shownthe solid.
is rotated about the xaxis to form a solid, use Simpson’s Rule with
rotating the region bounded If the given
to estimate the volume of the solid. (Write an expression involving only numbers, but
is....
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This note was uploaded on 07/31/2013 for the course MATH 42 taught by Professor Butscher,a during the Spring '07 term at Stanford.
 Spring '07
 Butscher,A
 Math, Calculus

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