Prove from the definition of the definite integral that[*z dx = 1 (10² - a²).xYou may freely use the following identity without proof:1+2+ + n =n(n+1)2

Answered: Image /qna-images/answer/afd26434-859d-45d6-830b-6a0d5dbacea3.jpg

Answered: Prove from the definition of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Prove from the definition of the definite integral that
[*z dx = 1 (10² - a²).
x
You may freely use the following identity without proof:
1+2+ + n =
n(n+1)
2

Expert Solution

Step 1: Solving the problem

$w e space h a v e space t o space f i n d space o u t integral subscript a superscript b x d x space W e space k n o w space t h a t space space integral subscript a superscript b f left parenthesis x right parenthesis d x equals left parenthesis b minus a right parenthesis limit as n rightwards arrow infinity of space 1 over n left parenthesis f left parenthesis a right parenthesis plus f left parenthesis a plus h right parenthesis plus f left parenthesis a plus 2 h right parenthesis... plus space f left parenthesis a space plus space left parenthesis n space minus space 1 right parenthesis space asterisk times space h right parenthesis space right parenthesis space space P u t t i n g space space a space equals space a space comma space b space equals space b space comma space h space equals space fraction numerator b minus a over denominator n end fraction comma space f left parenthesis x right parenthesis space equals space x$