MAT 1235 Calculus II Exam I Review

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Presentation transcript:

MAT 1235 Calculus II Exam I Review

Exam I Date and Time: 1/26 Monday Time: 1:45-2:50 Section , , 6.1 Total Points: 60 points

Bonus Points for Tutoring Please submit your record today.

Minimum Requirements

4.1 Familiar with the idea behind the area problem.

Definition

Idea: area under the graph of a function i th subinterval sample point

4.2 Definite Integrals Familiar with the limit definition of definite integrals with Riemann Sum. Familiar with the properties of the definite integrals. Able to estimate the values of definite integrals. You need to use the Closed Interval Method and other appropriate techniques and methods.

Properties of Definite Integrals

4.3 Fundamental Theorem of Calculus (FTC) Able to use part I of the FTC to differentiate definite integrals. Able to evaluate definite integrals by the part II of the FTC.

Fundamental theorem of Calculus Part I

Example (a) (b)

Example (a) (b)

Example (a) (b)

Example (a) (b)

Fundamental theorem of Calculus Part II

Indefinite Integrals Vs Definite Integrals

4.4 Familiar with the net change theorem. Able to find the displacement and distance traveled by a particle.

4.5 Able to use the substitution rule to evaluate indefinite and definite integrals. Notice the difference between the two. Able to simplify definite integrals of even and odd functions over symmetrical intervals.

The substitution Rule for Indefinite Integrals

Example

The substitution Rule for Definite Integrals

Example

Remark The procedures for indefinite and definite integrals are similar but different For definite integral, we need to change the upper and lower limits when using a substitution Do not change back to the original variable

5.1 Able to find the area of type I and type II regions.

Type I: Region Bounded Above/Below

Type II: Region Bounded Left/Right

Section 5.2, 5.3 Able to find the volume of solids using the disc and shell methods. Know how to formulate the volume if the axis of rotation is not the x- axis or y- axis.

Solid along the x-axis

Shell Method

Section 6.1 Able to find the derivatives of inverse functions.

Additional Info

Give Exact Answers know the trigonometric function values of special angles.

Grading Scheme: Disc Method

Grading Scheme: Shell Method

General Info Absolutely no share of calculators. Bring extra batteries, extra calculators. It is your responsibility to bring a workable calculator. You are expected to use correct notations. You are expected to make your arguments very carefully Make sure you put down the details of the solutions. No points will be given to answers alone. Make sure your work is neat, clear and easily readable or you will receive NO credits.

General Info No points will be given to graphs or graphical solutions. Make sure your solutions are complete and logically presented.

General Info Check and Recheck your solutions. Be sure to cross out any scratch works or unwanted materials. If more than one solution is given, no points will be given.

Calculator Calculators with more than184 K combined memory (RAM/Flash ROM) or symbolic computation ability are NOT allowed (e.g.TI-83 Plus Silver Ed., TI-89, TI-92 Casio FX-2.0 HP 38g, 39g, 40g, 48g/48g+/48gx, 49g). DO NOT store any information in your calculator.