Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

FinalThis

**preview**shows pages 1-2. to view the full**8 pages of the document.**MATH 2B: SAMPLE FINAL #1

•This exam consists of 14 questions and 100 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. (6 points) Suppose that R1

−1f(x)dx = 6,R4

1f(x)dx =−2and R1

−1h(x)dx = 9. Use this

information to compute the following.

a. R1

46f(x)dx

b. R1

−12f(x) + 3h(x)dx

c. R4

−1f(x)dx

2. (6 points)

a. Evaluate the following derivative

d

dx Zx2

sin(x)

t3tan(t)dt.

b. Let r(t)be the rate at which the world’s oil is consumed, where tis measured in years starting

at t= 0 representing January 1, 2000, and r(t)is measured in barrels per year. What does

R13

0r(t)dt represent and what are its units?

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3. (6 points) Evaluate Rx2tan−1x dx

4. (6 points) Evaluate Z1

xln(3x)dx

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5. (6 points) Evaluate Rsin5(x) cos2(x)dx

6. (6 points) Evaluate Z√x2−25

xdx, where x > 5

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