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 \(p\left(\frac{3}{2}\right)+\mathrm{C}=\)
- A \(0\)
- B \(8\)
- C \(\frac {-17}{2}\)
- D \(48\)
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 \(x=1\)…
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