UCe the Vmit de fi miおもn of rhc aefrile へとgral, im ; fcxi)x - 5fしょsdx」 to prove hat ハう fex) dx= - tu)dx
UCe the Vmit de fi miおもn of rhc aefrile へとgral, im ; fcxi)x - 5fしょsdx」 to prove hat ハう fex) dx= - tu)dx
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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Question
![**Use the limit definition of the definite integral,**
\[
\lim_{{n \to \infty}} \sum_{{i=1}}^{n} f(x_i) \Delta x = \int_{a}^{b} f(x) \, dx
\]
**to prove that**
\[
\int_{b}^{a} f(x) \, dx = - \int_{a}^{b} f(x) \, dx
\]
**Explanation:**
The image contains a mathematical procedure using the limit definition of definite integrals. It asks to prove a property of integrals: that reversing the limits of integration changes the sign of the integral's value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2ce945b-ebf8-47d5-81d6-18edb03d27a8%2Fe7e7bd6f-281f-4dc9-b80c-50e4202dbc86%2Fgitmlbn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Use the limit definition of the definite integral,**
\[
\lim_{{n \to \infty}} \sum_{{i=1}}^{n} f(x_i) \Delta x = \int_{a}^{b} f(x) \, dx
\]
**to prove that**
\[
\int_{b}^{a} f(x) \, dx = - \int_{a}^{b} f(x) \, dx
\]
**Explanation:**
The image contains a mathematical procedure using the limit definition of definite integrals. It asks to prove a property of integrals: that reversing the limits of integration changes the sign of the integral's value.
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