Unformatted text preview: Math 21B
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Discussion Sheet 2 1.) Determine the following indeﬁnite integrals (antiderivatives). 2324—1 $2+1 1:2
'. d b. d . '
a)/ $3 a: )/x+3 w c)/$3+1dm 2.) Evaluate the following deﬁnite integrals. % . 1 71’
a.) / cos m 65‘” d]: b.) / 5“” da: c.) / 5 sec2 3x d1:
0 0 ——1 3.) Set up a deﬁnite integral and compute the volume of a solid located between a plane
at x : 1 and a plane located at x = 5 if the cross—sectional area of the solid by a plane
perpendicular to the :c—axis at :r is 63:3 square centimeters. 4.) Evaluate the following. HINT: Use problem 34 on page 265.
20 15
i 21‘
) 2—0 3 b.) 2—2 2 c.) ”lingo— n 1:1 2 sin3$ arctanav
5.) Differentiate each : a.) F(:I:) :2 V1 + t2 dt b.) F(:c) :/ 5t2 dt
t — 100 an a: 6.) Find the average value of each of the following functions over the given interval. Draw a
sketch showing the connection between your answer and the deﬁnite integral. .))f(:z: :$3 +1 on b.) f( ):5+\/E on [0,4] [— 1, 1]
1
)If a/:( ﬂat )dmz3 and /:f(:r)d 2—2.Whatistheva1ueof /f(:r)d:1: 7
3 8.) A thin rod is 16 cm. long. Its density :3 cm. from its left end is given by 2 + ﬂ gm./cm. a.) Estimate the rod’s total mass by using four equal subdivisions and midpoints to
estimate densities.
b.) Set up a deﬁnite integral and compute the exact mass of the rod. 9.) Consider the following sequence of numbers : 1, 5, 9, 13, 17, 21, 25, Find the sum of
the Glst through the 127th numbers in this sequence. 10.) Use the limit deﬁnition of a deﬁnite integral to evaluate 1 2
a.) / 3:3 d3: b.) / e“C day
0 0
THE FOLLOWING PROBLEM IS FOR RECREATIONAL PURPOSES ONLY. 11.) Connect 6 toothpicks end—to—end to form 4 triangles. ...
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 Winter '09
 Kouba
 Calculus

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