Problem 2: Evaluate the following integrals:1(a) S4х-7-1 хdx0 x2+35(c) ;c) Sdx-32хdx(d) J2 x(In x)*3

Answered: Problem 2: Evaluate the following…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Problem 2: Evaluate the following integrals:
1
(a) S
4х-7
-1 хdx
0 x2+3
5
(c) ;
c) Sdx
-
32х
dx
(d) J2 x(In x)*
3

Expert Solution

Step 1

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the subpart to be solved".

Given integral:

$\int \frac{1}{4 x - 7} d x$

Substitute $(4 x - 7) = u$ and differentiate it w.r.t "x"

$\frac{d}{d x} (4 x - 7) = \frac{d u}{d x} 4 d x = d u d x = \frac{1}{4} d u$

The integral becomes

$\frac{1}{4} \int \frac{1}{u} d u$

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