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Integration Formula Sheet - Chapter 41 Class 41 Formulas Important

Question 1 Important Deleted for CBSE Board 2024 Exams

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Chapter 7 Class 12 Integrals

Serial order wise

Last updated at June 13, 2023 by Teachoo

Misc 40 Choose the correct answer If 𝑓(𝑎+𝑏−𝑥)=𝑓(𝑥), then ∫_𝑎^𝑏▒〖𝑥 𝑓(𝑥) 〗 𝑑𝑥 is equal to (A) (𝑎+𝑏)/2 ∫_𝑎^𝑏▒〖 𝑓(𝑏−𝑥) 〗 𝑑𝑥 (B) (𝑎+𝑏)/2 ∫_𝑎^𝑏▒〖 𝑓(𝑏+𝑥) 〗 𝑑𝑥 (C) (𝑏 −𝑎)/2 ∫_𝑎^𝑏▒〖 𝑓(𝑥) 〗 𝑑𝑥 (D) " " (𝑎+𝑏)/2 ∫_𝑎^𝑏▒〖 𝑓(𝑥) 〗 𝑑𝑥 Let I=∫_𝑎^𝑏▒〖𝑥 𝑓(𝑥) 〗 𝑑𝑥 ∴ I=∫_𝑎^𝑏▒〖(𝑎+𝑏−𝑥) 𝑓(𝑎+𝑏−𝑥) 〗 𝑑𝑥 I=∫_𝑎^𝑏▒〖(𝑎+𝑏−𝑥) 𝑓(𝑥) 〗 𝑑𝑥 I=∫_𝑎^𝑏▒〖(𝑎+𝑏) 𝑓(𝑥) 〗 𝑑𝑥−∫_𝑎^𝑏▒〖𝑥 𝑓(𝑥) 〗 𝑑𝑥 Adding (1) and (2) i.e (1) + (2) I+I=∫_𝑎^𝑏▒〖𝑥 𝑓(𝑥) 〗 𝑑𝑥+∫_𝑎^𝑏▒〖(𝑎+𝑏) 𝑓(𝑥) 〗 𝑑𝑥−∫_𝑎^𝑏▒〖𝑥 𝑓(𝑥) 〗 𝑑𝑥 2I=∫_𝑎^𝑏▒〖(𝑎+𝑏) 𝑓(𝑥) 〗 𝑑𝑥 2I=(𝑎+𝑏) ∫_𝑎^𝑏▒𝑓(𝑥) 𝑑𝑥 ∴ I=(𝑎 + 𝑏)/2 ∫_𝑎^𝑏▒𝑓(𝑥) 𝑑𝑥 ∴ Option D is correct .