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Ifx=int0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)...

`Ifx=int_0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)/(dx^2)=a y ,t h e nfin da`

A

3

B

6

C

9

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` x = int _(0)^(y) (dt)/(sqrt(1+9t^(2))` ,
` rArr (dx)/(dy) = 1/(sqrt(1+9y^(2)))` [ By Leibnitz rule]
which gives , ` (d^(2)y)/(dx^(2)) = (18y)/(2sqrt(1+9y^(2)))(dy)/(dx) = 9y `
` :. A = 9`
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