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Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2...

Let `f(0)=0a n dint_0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)i s` log 2 (b) log 7 (c) log 11 (d) log 13

A

`log 2`

B

`log 7`

C

`log 11`

D

`log 13`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `int_(0)^(2) f'(2t)e^(f(2t))dt=5`
Put `e^(f(2t))=y`
`:. 2f'(2t)e^(f(2t))dt=dy`
`:. 1/2 int_(e^(f(0)))^(e^(f(4)))dy=5`
or `int_(e^(f(0)))^(e^(f^(4))) dy =10`
or `e^(f(4))-e^(f(0))=10`
or `e^(f(4))=10+1=11`
or `f(4)=log11`
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