JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f:[1,\infty)\rightarrow\mathbb{R}\) be a differentiable function. If \(6\int_{1}^{x}f(t)dt=3xf(x)+x^{3}-4\) for all \(x\ge1\), then the value of \(f(2)-f(3)\) is
- A -4
- B -3
- C 4
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
\(6 \int_1^x f(t) d t=3 x f(x)+x^3-4\) Diff. both side \(6 f(x)=3 x f^{\prime}(x)+3 f(x)+3 x^2\) \(3 f(x)=3 x f^{\prime}(x)+3 x^2\) \(x \frac{d y}{d x}-y=-x^2\) \(\frac{x \frac{d y}{d x}-9}{x^2}=-1\) \(\Rightarrow \frac{ d }{ dx }\left(\frac{ y }{ x }\right)=-1\)…
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