JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f\) be a twice differentiable function on \(R\). If \(f^{\prime}(0)=4\) and \(f(x)+\int_{0}^{x}(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x\) then \((2 a+1)^{5} a^{2}\) is equal to \(\dots\dots\)
- A \(4\)
- B \(8\)
- C \(6\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(8\)
Step-by-step Solution
Detailed explanation
\(f(x)+\int_{0}^{x}(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right)\) \(\cos 2 x+\frac{2 x}{a}\) Here \(f(0)=2\) On differentiating equation \((i)\) w.r.t. \(x\) we get :…
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