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Text: Calculus. Early Transcendental Version by C.H. Edwards and D.E. Penney, 6th Edition, 2003.

General information:

Closed-text & closed-notes event. Calculators are not allowed (and not needed). The Handout containing recipes for trigonometric integrals and instructions for trigonometric substitutions can be used as a reference sheet.

Subject:

Techniques of integrations - the material considered in the course after Test 2

Concepts which should be under unconditional control:

• Elementary integral forms (13 integrals listed in the Handout containing basic integrals and differentiation rules).
• Method of u-substitution
• Integration by parts technique
• Evaluation of trigonometric integrals with the use of trigonometric identities
• Elimination of radicals in the integrands by trigonometric substitutions

Contents: Problems with Nos from 1 to 5

Evaluation of the integrals:

1. ...related to an elementary integral form
2. ...with an appropriate u-substitution
3. ...by integration by parts
4. ...with a suitable trigonometric identity
5. ...with the use of trigonometric subtitution
6. Bonus.

Sample problems:

1. 6.8: 35, 37, 43
2. 7.2: 11, 13, 15
3. 7.3: 3, 13, 15
4. 7.4: 19, 35, 39
5. 7.6: 5, 23, 29,

General information:

Closed-text & closed-notes event. Calculators are not allowed (and not needed). The Handout containing basic integral formulas and differentiation rules can be used as a reference sheet.

Subject:

Applications of the integral - the material considered in the course after Test 1

Concepts which should be under unconditional control:

• Method of setting up integral formulas
• Volumes by the method of cross-sections; solids of revolution; revolution about the x- and y-axes
• Length of a smooth curve
• Surface area of revolution
• Work done by a variable force
• Center of mass (centroid) of a plane region; moment about the x- and y-axes
• Natural logarithmic function and natural exponential function; general exponential function and general logarithmic function; differentiation and integration of these functions
• Inverse trigonometric functions and their derivatives

Contents: Problems with Nos from 1 to 6

1. Finding the volume of the solid of revolution
2. Finding the length of the smooth curve
3. Formulation of the integral giving the surface area of revolution
4. Finding the centroid of the plane region
5. Finding the derivative of a logarithmic or exponential function
6. Evaluation of the integral associated with a logarithmic or exponential function
7. Bonus.

Sample problems:

1. 6.2: 11, 17
2. 6.4: 21, 25
3. 6.4: 13, 19
4. 6.6: 13, 15
5. 6.7: 7, 13
6. 5.7: 29, 39

General information:

Closed-text & closed-notes event. Calculators are not allowed.

Subject:

The integral - the material considered so far in the course and covered by Chapter 5

Concepts which should be under unconditional control:

• Sums; Sigma notation; summation formulas.
• Definite integral as the limit of Riemann sum.
• Antidifferentiation; definite integral by definition (as a limit of a Riemann sum); the Fundamental Theorem of Calculus; major properties of the definite integral.
• Techniques of integration: power rule, generalized power rule, method of substitution. Basic integral formulas.
• Differentiation of definite integrals
• Area of a plane region

Contents: Problems with Nos from 1 to 5; No 4 consists of 2 similar problems:

1. Evaluation of a sum.
2. Evaluation of the definite integral through its definition (limit of a Riemann sum).
3. Evaluation of an indefinite integral.
4. Evaluation of the definite integrals.
5. Differentiation of the definite integral.
6. Bonus.

Sample problems:

1. 5.3: 23, 25
2. 5.4: 45, 47
3. 5.2: 9, 21
4. (a) 5.5: 23, 35; (b) 5.7: 55, 59
5. 5.6: 57, 59

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Last modified: 6:30 pm; Tue, Feb 28, 2006