{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HH_Sec_7_2

HH_Sec_7_2 - Math 10B Lecture Examples Section 7.2...

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 7.2. Integration by parts† Example 1 (a) Find the antiderivative diﬀerentiation. Answer: (a) x cos x dx. (b) Check the result by d (x sin x + cos x) = x cos x. dx x cos x dx = x sin x + cos x + C (b) Product Rule: Example 2 What is the area of the region between y = xe−x and the x-axis for 0 ≤ x ≤ 4? Answer: Figure A2 • [Area] = 1 − 5e−4 y 0.4 0.2 y = xe−x 2 Figure A2 4 x Example 3 Find the antiderivative Answer: (a) x3 ln x dx. x3 ln x dx = 5 14 x 4 1 ln x − 16 x4 + C Example 4 Evaluate 1 5 ln (2x) dx. Answer: 1 ln(2x) dx = 5 ln(10) − ln(2) − 4 Example 5 Find the indeﬁnite integral Answer: (ln x)4 x dx. (ln x)4 x dx = 1 (ln x)5 5 +C Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡ Section 8.1: Examples 1 and 2 notes to accompany Section 7.2 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

{[ snackBarMessage ]}

Ask a homework question - tutors are online