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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let ' f ' is a function, continuous on such that f(x) ≤ 5 \; x ∈...

Let '

f

' is a function, continuous on such that

f(x) \leq \sqrt{5} \; \forall x \in

and

f(x) \leq \frac{2}{x} \; \forall x \in [\frac{1}{2}, 1]

then the smallest '

a

' for which

\int_0^1 f(x) dx \leq a

holds for all '

f

' is:

Options

A $\sqrt{5}$
B $\frac{\sqrt{5}}{2} + 2\ln 2$
C $2 + \ln \left(\frac{\sqrt{5}}{2}\right)$
D $2 + 2\ln \left(\frac{\sqrt{5}}{2}\right)$

Correct answer

D. $2 + 2\ln \left(\frac{\sqrt{5}}{2}\right)$

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