6 3x 12 find the partial fractions decomposition of

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: he general antiderivative F (x) of a certain rational function f (x) is given by F (x) = 1 x3 (2x + 5) ln + C. 6 (3x − 1)2 Find the partial fractions decomposition of the function f (x) and hence find f (x). [hint: Use log rules first to simplify F (x).] challenge: 9. Suppose that f is an increasing, differentiable function for a ≤ x ≤ b, where b > a > 0. a) Sketch a possible graph of y = f (x) on [a, b]. Outline the rectangular regions with areas af (a) and bf (b) on the given diagram. b) Give a geometric argument explaining why b bf (b) − af (a) = f (b) f −1 (y ) dy. f (x)dx + a f (a ) (Explain why f −1 exists.) c) Verify the result in c) as follows: (i) Use integration by parts to show that, for any differentiable function f , f (x)dx = xf (x) − xf (x) dx. (ii) Integrate the result in (i) from a to b and subsitute x = f −1 (y ) in the right-hand integral to achieve the final result. Math 138 Assignment 1 Addendum Using Maple for Integration, Partial Fractions and Arc Length (Classic Version for Windows) Author: B. A. Forrest Send comments or corrections to email:...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online