Trigonometric Integrals

Author: John J Weber III, PhD Corresponding Textbook Sections:

• Section 7.2 – Trigonometric Integrals

Expected Educational Results

• Objective 04–01: I can evaluate an indefinite trigonometric integral.

• Objective 04–02: I can evaluate a definite trigonometric integral using FTC-II.

Bloom’s Taxonomy

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Trigonometric Integrals

Investigation 08

Explain why $u$$u$-substitution a NOT a valid method for the following integrals:

1. ${\displaystyle \int {\cos }^2(x)dx}$$\displaystyle \int{\cos^2{\!(x)}\,dx}$

2. ${\displaystyle \int {\sin }^2(x)dx}$$\displaystyle \int{\sin^2{\!(x)}\,dx}$

3. ${\displaystyle \int {\sin }^2(x){\cos }^2(x)dx}$$\displaystyle \int{\sin^2{\!(x)}\,\cos^2{\!(x)}\,dx}$

4. ${\displaystyle \int {\sin }^2(x){\cos }^4(x)dx}$$\displaystyle \int{\sin^2{\!(x)}\,\cos^4{\!(x)}\,dx}$

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Created: Tuesday, 1 September 2020 03:36 EDT Last Modified: Tuesday, 16 August 2022 - 20:59 (EDT)