Last updated at March 29, 2023 by Teachoo
This question is similar to Misc 43 (MCQ) - Chapter 7 Class 12 - Integrals
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Question 4 β«1_(π + π)^(π + π)βγ π(π₯) ππ₯γ is equal to β«1_(π )^(π )βγπ(π₯βπ) ππ₯γ (B) β«1_(π )^(π )βγπ(π₯+π) ππ₯γ (C) β«1_(π )^(π )βγπ(π₯) ππ₯γ (D) β«1_(π βπ)^(πβπ )βγπ(π₯) ππ₯γ β«1_(π + π)^(π + π)βγ π(π₯) ππ₯γ Putting π=π+π Differentiating w.r.t. π₯ ππ₯=ππ‘ Now, when π varies from a + c to b + c then π varies from a to b Therefore β«1_(π + π)^(π + π)βγ π(π₯) ππ₯γ =β«_π^πβπ(π‘+π)ππ‘ Changing variables β using Property 1 =β«_π^πβπ(π+π)π π So, the correct answer is (b)
