VIII. Integration

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VIII.1. Decomposition and Integration

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VIII.1.1. The Fundamental Theorem of Calculus

VIII.1.2. Areas Bounded by Functions

VIII.1.3. The Length of a Curve

VIII.1.4. Application of Symmetry Principle: Solids of Revolution

VIII.1.5. Application of Symmetry Principle: Surfaces of Revolution

VIII.1.6. Integration of Vector Valued Functions

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VIII.2. Methods of Approximation

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VIII.2.1. Orders of Approximation

VIII.2.2. Improper Integrals

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VIII.3. Transformation of Integrals

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VIII.3.1. The Method of Undetermined Coefficients

VIII.3.2. Bijections between Domains of Integration

VIII.3.3. Integration by Substitution

VIII.3.4. Coordinate Changes and Integrals over Paths

VIII.3.5. Integration by Parts

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VIII.4. Creation of Functions

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VIII.4.1. Using the Integral to Define Functions

VIII.4.2. The Convolution of Functions

VIII.4.3. Differentiating Integrals

VIII.4.4. Trigonometric and Hyperbolic Functions

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VIII.5. Frameworks for Calculation

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VIII.5.1. The Decomposition of Rational Functions

VIII.5.2. Antiderivatives of Rational Functions

VIII.5.3. Weierstrass Substitution

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VIII.6. Applications to Motion and Geometry

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VIII.6.1. Dynamical Evolution

VIII.6.2. Work Integrals

VIII.6.3. Areas Bounded by Paths

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Worksheets

Optional: For students and instructors looking for further exploration.

Worksheet VIII.1: Title

Worksheet VIII.2: Title

Worksheet VIII.3: Title

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© Copyright 2023 by the POC Writing Team: Bryan Carrillo, Dylan Noack, project PI Yat Sun Poon, and lead author David Weisbart.All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from David Weisbart and the POC Writing Team.

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