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Math 1432 DAY 20

Dr. Melahat Almus

almus@math.uh.edu

OFFICE HOURS: MW12-11:30pm, F:12-1pm at 212 PGH

Review for Test 3

Material: Chapter 8,

Time: 50 minutes

Number of questions: ??TBA

The grade you’ll see right away will be for MC part only.

Do not be late for your test.

If you miss your test, try to reschedule. If you can’t, you will get a 0. Final replaces one missed test (or your lowest test – if you haven’t missed any tests).

Take practice test 3! 5% of your best score will be added to your test grade.

How to study? Go over class notes, rework past quizzes, emcfs and poppers. Work on the review sheet posted on my website and take the practice test.

What to know:

Integration (u-sub)

Integration by parts,

Integrating using trig substitution,

Integrals of trig powers,

Integrating using partial fractions, Partial Fraction Decomp.

Approximations; Left endpoint (L_n), Right endpoint (R_n), midpoint (M_n), Trapezoidal rule (T_n), Simpson’s Rule (S_n).

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1. Integrate:

2 cos 10x x dx

Also solve:

24

1

10 xxe dx

2arctan( )x dx

Just know: x x xxe dx xe e C and ln lnxdx x x x C

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2. Integrate:

a) 3 2cos sinx x dx

b) 4 2sec tanx xdx

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3. Integrate:

a) 2 2

1

4dx

x x

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b) 2

1

9dx

x

c) An integral is computed using trig substitution 4sinx . The integral is: 2 sin cos tan C . Express the answer in terms of “x”.

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Section 8.4 Rational Functions; Partial Fractions

4. Give the form of PFD:

2 1 2

x

x x

22

4 1

3 2 1

x

x x x

5.

2

2

5 2

1 1

x xdx

x x

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6.

2

2

2

1 2

xdx

x x

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8.5 Numerical Integration

Left endpoint (Ln), Right endpoint (Rn), midpoint (Mn), Trapezoidal rule (Tn), Simpson’s Rule (Sn).

Know these methods and how to compare them in terms of errors. Solve the problems on the review sheet posted on course website.

For instance: Compare L_4, R_4, T_4 and exact integral for a positive function

* increasing, concave down

*decreasing, concave up

*decreasing, concave down.

(Solve popper questions in Day 19)

7. Approximate 5

2

1

1x dx using

a) Simpson’s method with n=4.

b) using Trapezoid method with n=4.

Exercise: Find an upper bound for the error if 4T is used to approximate 1

3

0

xe dx