## If x= β« 0^y dt/β(1 + 9t^2) and (d^2 y) / (dx^2 ) = ay, then a is equal to

## (A) 3Β

## (B) 6Β

## (C) 9Β

## (D) 1

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Chapter 7 Class 12 Integrals

Serial order wise

Last updated at March 16, 2023 by Teachoo

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Question 6 If π₯= β«1_0^π¦βγ ππ‘/β(1 + 9π‘^2 )γ and (π^2 π¦)/(ππ₯^2 )=ππ¦, then π is equal to 3 (B) 6 (C) 9 (D) 1 Since π₯= β«1_0^π¦βγ ππ‘/β(1 + 9π‘^2 )γ Changing variable from t to y π₯= β«1_0^π¦βγ ππ¦/β(1 + 9π¦^2 )γ It means x is a function of y So, we can write π π/π π=π/β(π + ππ^π ) And, ππ/ππ±=β(1 + 9π¦^2 ) Differentiating again w.r.t x (π^π π)/(ππ±^π )=π/(πβ(1 + 9π¦^2 )) Γπ (ππ^π )/π π (d^2 π¦)/(dx^2 )=1/(2β(1 + 9π¦^2 )) Γ 9 Γ 2π¦ Γπ π/π π Putting value of ππ¦/ππ₯ (π^π π)/(ππ±^π )=π/(πβ(1 + 9π¦^2 )) Γ π Γ ππ Γβ(1 + 9π¦^2 ) (π^π π)/(ππ±^π )=ππ Thus, a = 9 So, the correct answer is (c)