JEE Mains · Maths · STD 12 - 9. differential equations
Let a differentiable function \(f\) satisfy \(f ( x )+\int \limits_3^{ x } \frac{ f ( t )}{ t } dt =\sqrt{ x +1}, x \geq 3\). Then \(12 f (8)\) is equal to:
- A \(34\)
- B \(19\)
- C \(17\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(17\)
Step-by-step Solution
Detailed explanation
Differentiate w.r.t. x \(f^{\prime}(x)+\frac{f(x)}{x}=\frac{1}{2 \sqrt{x+1}}\) \(\text { I.F. }=e^{\int \frac{1}{x} d x}=e^{\ln x}=x\) \(x f(x)=\int \frac{x}{2 \sqrt{x+1}} d x\) \(x+1=t^2\) \(=\int \frac{t^2-1}{2 t} 2 t d t\) \(x f(x)=\frac{t^3}{3}-t+c\)…
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