Let f:[1,∞)toR be a differentiable function such that f(1)=1/3 and 3displaystyleint_1^x f(t)dt = x f(x)-(x^3)/3, x∈[1,∞). Let e denote the base of the natural logarithm. Then the value of f(e) is

Let f:[1,∞)toR be a differentiable function such that… — JEE Advanced 2023 Mathematics PYQ

JEE Advanced 2023 · Paper 2

Let

f:[1,\infty)\to\mathbb{R}

be a differentiable function such that

f(1)=\dfrac{1}{3}

and

3\displaystyle\int_1^x f(t)dt = x\,f(x)-\dfrac{x^3}{3}

x\in[1,\infty)

. Let

e

denote the base of the natural logarithm. Then the value of

f(e)

Show answer

Correct option: C

[JEE Advanced 2023 · Paper 2]

Practise Differential Equations the way it is asked

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