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If the area bounded by the x-axis, the c...

If the area bounded by the x-axis, the curve `y=f(x), (f(x)gt0)" and the lines "x=1, x=b " is equal to "sqrt(b^(2)+1)-sqrt(2)" for all "bgt1,` then find f(x).

Text Solution

Verified by Experts

The correct Answer is:
`(x)/(sqrt(x^(2)+1))`
`"Area "=int_(1)^(b)f(x)dx=sqrt(b^(2+1))-sqrt(2)`
Differentiating both sides w.r.t. b, we get
`f(b)=(b)/(sqrt(b^(2)+1))`
`therefore" "f(x)=(x)/(sqrt(x^(2)+1))`
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