Consider the integralI= ¹₁ (Inx) (arccosx) dxLet the primary branch of I be expressedas a+bi. Determine b-a

The given integral is:The primary branch of I be expressed as a+bi.To find: b-a.Formula used:

Answered: Consider the integral I=ſ¹₁(lnx)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

Consider the integral
I= ¹₁ (Inx) (arccosx) dx
Let the primary branch of I be expressed
as a+bi. Determine b-a

Expert Solution

Step 1: Introduction

The given integral is:

$text I end text equals integral subscript negative 1 end subscript superscript 1 open parentheses ln open parentheses x close parentheses close parentheses open parentheses a r c cos open parentheses x close parentheses close parentheses space d x$

The primary branch of I be expressed as a+bi.

To find: b-a.

Formula used:

$integral u v space d x equals u integral v d x minus integral open parentheses fraction numerator d over denominator d x end fraction u minus integral v space d x close parentheses d x integral ln open parentheses x close parentheses d x equals x ln open parentheses x close parentheses minus x plus C integral a r c cos open parentheses x close parentheses d x equals negative fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction plus C$