Chapter 7 Class 12 Integrals
Concept wise

Ex 7.10, 19 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by

Slide51.JPG

Slide52.JPG

Share on WhatsApp

Transcript

Ex 7.10, 19 Show that ∫_0^𝑎▒𝑓(𝑥) 𝑔 (𝑥) 𝑑𝑥=2∫_0^𝑎▒𝑓(𝑥) 𝑑𝑥, if f and g are defined as 𝑓(𝑥)=𝑓(𝑎−𝑥) and 𝑔(𝑥)+𝑔(𝑎−𝑥)=4 Let I =∫_0^𝑎▒𝑓(𝑥) 𝑔(𝑥) 𝑑𝑥 I =∫_0^𝑎▒𝑓(𝑥) [4−𝑔(𝑎−𝑥)] 𝑑𝑥 I = ∫_0^𝑎▒[4.𝑓(𝑥)−𝑓(𝑥)𝑔(𝑎−𝑥)] 𝑑𝑥 I = 4∫_0^𝑎▒〖𝑓(𝑥)𝑑𝑥−∫_0^𝑎▒〖𝑓(𝑥) 𝑔(𝑎−𝑥) 〗〗 𝑑𝑥 I = 4∫_0^𝑎▒〖𝑓(𝑥)𝑑𝑥−∫_0^𝑎▒〖𝑓(𝑎−𝑥) 𝑔(𝑎−(𝑎−𝑥)) 〗〗 𝑑𝑥 I = 4∫_0^𝑎▒〖𝑓(𝑥)𝑑𝑥−∫_0^𝑎▒〖𝑓(𝑥) 𝑔(𝑥) 〗〗 𝑑𝑥 I =4∫_0^𝑎▒〖𝑓(𝑥)𝑑𝑥−I〗 I +I=4∫_0^𝑎▒𝑓(𝑥)𝑑𝑥 2I=4∫_0^𝑎▒𝑓(𝑥)𝑑𝑥 I=2∫_0^𝑎▒𝑓(𝑥)𝑑𝑥 ∴ ∫_0^𝑎▒〖𝑓(𝑥) 𝑔(𝑥) 〗 𝑑𝑥=2∫_0^𝑎▒𝑓(𝑥)𝑑𝑥 Hence Proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo