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CBSE Class 12 · 2023 · Differential EquationsMultiple Choice

If

\frac{d}{d x} f (x) = 2 x + \frac{3}{x}

and

f (1) = 1

, then

f (x)

is:

(A) $x^{2} + 3 lo g ∣ x ∣ + 1$
(B) $x^{2} + 3 lo g ∣ x ∣$ ✓ Correct
(C) $2 - \frac{3}{x ^{2}}$
(D) $x^{2} + 3 lo g ∣ x ∣ - 4$

Answer: (B)

Solution

Integrate the given derivative:

f (x) = \int (2 x + \frac{3}{x}) d x = x^{2} + 3 lo g ∣ x ∣ + C

Apply

f (1) = 1

:

1 = 1 + 3 lo g 1 + C \Rightarrow C = 0

f (x) = x^{2} + 3 lo g ∣ x ∣

CBSE Class 12 Board · 2023 · Single correct option

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