JEE Mains · Maths · STD 12 - 9. differential equations
Let \(f\) be a differentiable function satisfying
\(f(x)=1-2x+\int_{0}^{x}e^{(x-t)}f(t)dt, x\in R\) and let
\(g(x)=\int_{0}^{x}(f(t)+2)^{15}(t-4)^{6}(t+12)^{17}dt, x\in R.\)
If p and q are respectively the points of local minima and local maxima of g, then the value of \(|p+q|\) is equal to ___ .
- A 9
- B 15
- C 12
- D 6
Answer & Solution
Correct Answer
(A) 9
Step-by-step Solution
Detailed explanation
\(f(x)=1-2 x+e^x \int_0^x e^{-t} f(t) d t\) \(e^{-x} f(x)=(1-2 x) e^{-x}+\int_0^x e^{-t} f(t) d t\) \(e^{-x} f^{\prime}(x)-e^{-x} f(x)=-2 e^{-x}+(1-2 x) e^{-x}(-1)+e^{-x} f(x)\) \(f^{\prime}(x)-2 f(x)=2 x-3\) \(\frac{d y}{d x}-2 y=2 x-3\)…
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