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Integration Techniques & Applications

This course outline covers integration concepts including anti-differentiation, indefinite integrals, and formulas for powers, trigonometric, exponential, and hyperbolic functions. It also covers integration techniques such as product/powers of sines and cosines, trigonometric substitution, algebraic substitution, integration by parts, and integration of rational fractions. Finally, it discusses definite integrals including properties, applications to plane areas, lengths, volumes, and double integration. The reference material is a 1983 calculus textbook.

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MhiaBuenafe
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102 views1 page

Integration Techniques & Applications

This course outline covers integration concepts including anti-differentiation, indefinite integrals, and formulas for powers, trigonometric, exponential, and hyperbolic functions. It also covers integration techniques such as product/powers of sines and cosines, trigonometric substitution, algebraic substitution, integration by parts, and integration of rational fractions. Finally, it discusses definite integrals including properties, applications to plane areas, lengths, volumes, and double integration. The reference material is a 1983 calculus textbook.

Uploaded by

MhiaBuenafe
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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A.

Course Outline
1. Integration Concepts/Formulas
a) Anti-differentiation
b) Indefinite Integrals
c) Simple Power Formula
d) Integration by substitution
e) Integration of Trigonometric Functions
f) Integration of Exponential Functions
g) Integration of Hyperbolic Functions (sinh u & cosh u only)
h) Application of Indefinte Integration
2. Integration Techniques
a) Product of Sines and cosines
b) Powers of Sines and Cosines
c) Trigonometric Substitution
d) Additional standard Formulas
e) Integrands Involving Quadratic Expressions
f) Algebraic Substitution
g) Integration involving Quadratic Expressions
h) Integration by Parts
i) Integration of Rational Fractions
3. The Definite Integral
a) Some Properties of the definite Integral
1. Fundamental Theorems of Integral calculus
2. The Wallis formula
b) Some Applications of the Definite Integral
1. Plane Areas
a. Area Under a Curve
b. Area Between Two Curves
2. Centroid of a Plane Area
3. Length of Arc
4. Area of a Surface of Revolution
c) Other Applications
1. Volume of a Solid of Revolution
2. Hydrostatic Pressure
3. Work
d) Double Integration

B. Reference:
Feliciano, Florentino T and Uy, Fausto B. Differential and Integral
Calculus Merriam and Webster Bookstore, Inc. manila Philippines 1983

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