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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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

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.