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Let y=f(x) be satisfying differential eq...

Let `y=f(x)` be satisfying differential equation `e^(-x^(2))(dy)/(dx)=2xy^(2)` such that `f(0)=(1)/(2)`
Which of the following statements is correct about `f(x)`?

A

(a) `int_(0)^(1)f(x)dxlt(1)/(2)`

B

(b) Range of `f(x)` is `(0,(1)/(2)]`

C

(c) `(e+1)int_(0)^(1)f(x)dxgt1`

D

(d) None of these.

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)` is increasing in `(0.,1)` and `f(0)=(1)/(2)`
`impliesint_(0)^(1)f(x)dxgt(1)/(2)`
And `implies(e+1)int_(0)^(1)f(x)dxgt(e+1)/(2)gt1`
Hence (C) option is correct.
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