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TS EAMCET · Maths · Indefinite Integration

If \(\frac{x^4}{(x-1)(x-2)(x-3)}=p(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}\) then \(p\left(\frac{3}{2}\right)+\mathrm{C}=\)

  1. A \(0\)
  2. B \(8\)
  3. C \(\frac {-17}{2}\)
  4. D \(48\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(48\)

Step-by-step Solution

Detailed explanation

\(\frac{x^4}{(x-1)(x-2)(x-3)}=P(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}\). \(\begin{aligned} \Rightarrow \quad x^4=P(x) \cdot(x-1) & (x-2)(x-3)+A(x-2)(x-3) \\ & +B(x-1)(x-3)+C(x-1)(x-2)\end{aligned}\) Put \(x=1\)…