Check sibling questions

∫ (a + c)^(b + c)  f(x) dx is equal to

(A) ∫ (a )^(b)  f(x - c)   

(B) ∫ (a )^(b) f(x + c) dx 

(C) ∫(a )^(b) f(x) dx    

(D) ∫ (a - c)^(b - c) (x) dx    

This question is similar to Misc 43 (MCQ) - Chapter 7 Class 12 - Integrals

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Transcript

Question 4 ∫1_(π‘Ž + 𝑐)^(𝑏 + 𝑐)β–’γ€– 𝑓(π‘₯) 𝑑π‘₯γ€— is equal to ∫1_(π‘Ž )^(𝑏 )▒〖𝑓(π‘₯βˆ’π‘) 𝑑π‘₯γ€— (B) ∫1_(π‘Ž )^(𝑏 )▒〖𝑓(π‘₯+𝑐) 𝑑π‘₯γ€— (C) ∫1_(π‘Ž )^(𝑏 )▒〖𝑓(π‘₯) 𝑑π‘₯γ€— (D) ∫1_(π‘Ž βˆ’π‘)^(π‘βˆ’π‘ )▒〖𝑓(π‘₯) 𝑑π‘₯γ€— ∫1_(π‘Ž + 𝑐)^(𝑏 + 𝑐)β–’γ€– 𝑓(π‘₯) 𝑑π‘₯γ€— Putting 𝒙=𝒕+𝒄 Differentiating w.r.t. π‘₯ 𝑑π‘₯=𝑑𝑑 Now, when 𝒙 varies from a + c to b + c then 𝒕 varies from a to b Therefore ∫1_(π‘Ž + 𝑐)^(𝑏 + 𝑐)β–’γ€– 𝑓(π‘₯) 𝑑π‘₯γ€— =∫_π‘Ž^𝑏▒𝑓(𝑑+𝑐)𝑑𝑑 Changing variables – using Property 1 =∫_𝒂^𝒃▒𝒇(𝒙+𝒄)𝒅𝒙 So, the correct answer is (b)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.