Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.