Question:medium

Match List-I with List-II 

List-I\(F(x)\)List-IIParticular Integral Rule
A\(F(x)=e^{ax}\)III\(\dfrac{e^{ax}}{f(a)}, \quad f(a)\neq 0\)
B\(F(x)=\sin ax\)II\(\dfrac{\sin ax}{f(-a^2)}\)
C\(F(x)=xe^{ax}\)I\(\left(\dfrac{x}{f(a)}-\dfrac{f'(a)}{[f(a)]^2}\right)e^{ax}, \quad f(a)\neq 0\)
D\(F(x)=\cos ax\)IV\(D^2\) is replaced by \(-a^2\) in \(f(D)\)

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For \(e^{ax}\), replace \(D\) by \(a\); for \(\sin ax\) and \(\cos ax\), replace \(D^2\) by \(-a^2\).
Updated On: May 20, 2026
  • A-I, B-II, C-III, D-IV
  • A-III, B-IV, C-I, D-II
  • A-III, B-II, C-I, D-IV
  • A-I, B-IV, C-III, D-II
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The Correct Option is C

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