Show that if f is Riemann integrable [a, b] and f(r) 0 for all r € [a, b], on f(x) dr 2 0.
Show that if f is Riemann integrable [a, b] and f(r) 0 for all r € [a, b], on f(x) dr 2 0.
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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![Show that if \( f \) is Riemann integrable on \([a, b]\) and \( f(x) \geq 0 \) for all \( x \in [a, b]\), then
\[
\int_a^b f(x) \, dx \geq 0.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff906d8fa-9b6a-4046-ba2d-f959fe6282ae%2Fbe72e0c5-33a2-41ac-9edc-efcf97634cff%2Fhblfdy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that if \( f \) is Riemann integrable on \([a, b]\) and \( f(x) \geq 0 \) for all \( x \in [a, b]\), then
\[
\int_a^b f(x) \, dx \geq 0.
\]
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