If f(x)=∫xa 1/f(x) dx (x>0) and ∫1a 1/f(x) dx=√2,then f(50) is:
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3 Answers
1357f'(x)=1/f(x)
f'(x)f(x)=1
integrating it
[f(x)]2/2=x+c
given f(1)=√2, so c=0
so [f(x)]2=2x
[f(50)]2=100
f(50)=±10
263how are you getting f(1)=√2.I am getting f(1) - f(a)=√2 from the 2nd condition.
- Manish Shankar From first equationUpvote·0· Reply ·2014-07-18 01:35:31
187maybe it's because f(a)=∫aa 1/f(x)dx, lower limit =upper limit, thus f(a)=0.