HH_Sec_7_1

# HH_Sec_7_1 - (9/30/08) Math 10B. Lecture Examples. Section...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (9/30/08) Math 10B. Lecture Examples. Section 7.1. Integration by substitution† Example 1 Find the antiderivative Answer: (x2 + 1)5 (2x) dx. 1 (x2 + 1)5 (2x) dx = 6 (x2 + 1)6 + C Example 2 Perform the integration Answer: x3 x4 + 16 dx. √ √ x3 x4 + 16 dx = 14 (x 6 + 16)3/2 + C Example 3 Find the antiderivative Answer: √ cos( x) √ dx. x √ √ cos( x) x +C dx = 2 sin √ x Example 4 Find the area of the region in Figure 1. y 3 2 1 y= 10x (x2 + 1)2 FIGURE 1 1 2 3 x Answer: [Area] = 9 2 1 Example 5 Evaluate 0 1 sin(π x) dx. 2 Answer: 0 sin(πx) dx = 1 π Example 6 Evaluate 0 1 e−2x dx. 1 (1 − e−2 ) 2 Answer: 0 e−2x dx = Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡ Section 6.8: Examples 1 through 5 Section 7.1: Example 4 notes to accompany Section 7.1 of Calculus by Hughes-Hallett et al. chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. ‡ The † Lecture 1 ...
View Full Document

## This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

Ask a homework question - tutors are online
The text passage contains multiple mathematical questions, each followed by an answer. The questions are related to integration by substitution, and the answers are provided in the form of antiderivatives or evaluated integrals.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
HH_Sec_7_1

# HH_Sec_7_1 - (9/30/08) Math 10B. Lecture Examples. Section...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (9/30/08) Math 10B. Lecture Examples. Section 7.1. Integration by substitution† Example 1 Find the antiderivative Answer: (x2 + 1)5 (2x) dx. 1 (x2 + 1)5 (2x) dx = 6 (x2 + 1)6 + C Example 2 Perform the integration Answer: x3 x4 + 16 dx. √ √ x3 x4 + 16 dx = 14 (x 6 + 16)3/2 + C Example 3 Find the antiderivative Answer: √ cos( x) √ dx. x √ √ cos( x) x +C dx = 2 sin √ x Example 4 Find the area of the region in Figure 1. y 3 2 1 y= 10x (x2 + 1)2 FIGURE 1 1 2 3 x Answer: [Area] = 9 2 1 Example 5 Evaluate 0 1 sin(π x) dx. 2 Answer: 0 sin(πx) dx = 1 π Example 6 Evaluate 0 1 e−2x dx. 1 (1 − e−2 ) 2 Answer: 0 e−2x dx = Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡ Section 6.8: Examples 1 through 5 Section 7.1: Example 4 notes to accompany Section 7.1 of Calculus by Hughes-Hallett et al. chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. ‡ The † Lecture 1 ...
View Full Document

## This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

Ask a homework question - tutors are online
user
The text passage contains multiple mathematical questions, each followed by an answer. The questions are related to integration by substitution, and the answers are provided in the form of antiderivatives or evaluated integrals.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS