w10exam1

# 4 to estimate the volume obtained by rotating

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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 y-axis 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 y-axis 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 x-axis 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 x-axis 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.

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