Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows page 1. to view the full**5 pages of the document.**MATH 2B: SAMPLE MIDTERM #1

•This exam consists of 5 questions and 85 total points.

•Read the directions for each problem carefully and answer all parts of each problem.

•Please show all work needed to arrive at your solutions (unless instructed otherwise). Label

graphs and deﬁne any notation used. Cross out incorrect scratch-work.

•No calculators or other forms of assistance are allowed. Do not check your cell phones

during the exam.

•Clearly indicate your ﬁnal answer to each problem.

1. (15 points)

a. Estimate the area under the graph of f(x) = x2+xfrom x= 0 to x= 3 using 3 approxi-

mating rectangles and left endpoints.

b. Estimate the area under the graph of f(x) = x−1from x= 0 to x= 6 using 3 rectangles

and midpoints.

c. Find an expression for the area under the graph of f(x) = x2+xfrom x= 2 to x= 5 as a

limit of Riemann sums. (You do not need to evaluate the limit.)

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2. (15 points) Evaluate each of the following indeﬁnite integrals.

a. Rx√3x2−1dx

b. Z1−sin2(x)

cos xdx

c. Rsin(7θ+ 5) dθ

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