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Let `y=f(x)` be satisfying differential equation `e^(-x^(2))(dy)/(dx)=2xy^(2)` such that `f(0)=(1)/(2)` Q. Which of the following statement is correct about `f(x)`?A. `int_(0)^(1)f(x)dxlt(I)/(2)`B. Range of `f(x)` is `(0,(1)/(2)]`C. `(e+1)int_(0)^(1)f(x)dxgt1`D. None of these. |
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Answer» Correct Answer - 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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