Let f:[21,1]→R (the set of all real numbers) be a positive, non-constant, and differentiable function such that fprime(x)<2f(x)andf(21)=1 . Then the value of ∫211f(x)dx lies in the interval (a)(2e−1,2e) (b) (3−1,2e−1)(c)(2e−1,e−1) (d) (0,2e−1)

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Let {f}:{[{{1}}{{2}},{1}]}{R} (the set of all real numbers) be

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Let $f : [\frac{1}{2}, 1] \to R$ (the set of all real numbers) be a positive, non-constant, and differentiable function such that $f^{p r i m e} (x) < 2 f (x) a n d f (\frac{1}{2}) = 1$ . Then the value of $\int_{\frac{1}{2}}^{1} f (x) d x$ lies in the interval (a) $(2 e - 1, 2 e)$ (b) $(3 - 1, 2 e - 1)$ (c) $(\frac{e - 1}{2}, e - 1)$ (d) $(0, \frac{e - 1}{2})$

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Let

f : [\frac{1}{2}, 1] \to R

(the set of all real numbers) be a positive, non-constant, and differentiable function such that

f^{p r i m e} (x) < 2 f (x) a n d f (\frac{1}{2}) = 1

. Then the value of

\int_{\frac{1}{2}}^{1} f (x) d x

lies in the interval (a)

(2 e - 1, 2 e)

(b)

(3 - 1, 2 e - 1)

(c)

(\frac{e - 1}{2}, e - 1)

(d)

(0, \frac{e - 1}{2})

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Question Text	Let $f : [\frac{1}{2}, 1] \to R$ (the set of all real numbers) be a positive, non-constant, and differentiable function such that $f^{p r i m e} (x) < 2 f (x) a n d f (\frac{1}{2}) = 1$ . Then the value of $\int_{\frac{1}{2}}^{1} f (x) d x$ lies in the interval (a) $(2 e - 1, 2 e)$ (b) $(3 - 1, 2 e - 1)$ (c) $(\frac{e - 1}{2}, e - 1)$ (d) $(0, \frac{e - 1}{2})$
Answer Type	Video solution: 1
Upvotes	150