definite integral

If f(x)=∫xa 1/f(x) dx (x>0) and ∫1a 1/f(x) dx=√2,then f(50) is:

3 Answers

1357
Manish Shankar ·

f'(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

263
Sushovan Halder ·

how are you getting f(1)=√2.I am getting f(1) - f(a)=√2 from the 2nd condition.

187
Swastik Haldar ·

maybe it's because f(a)=∫aa 1/f(x)dx, lower limit =upper limit, thus f(a)=0.

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