Q.1 (B) (ii) State whether true or false: If ∫x/(1+x)(2+x) dx=∫(A/1+x+B/2+x)dx then A = 1, B = 2.

Answer: False x=A(2+x)+B(1+x) . Put x=-1 : -1=A(1)⇒ A=-1 . Put x=-2 : -2=B(-1)⇒ B=2 . So A=-1,\ B=2 , not A=1 .

State whether true or false: If \(\int\frac{x}{(1+x)(2+x)}\,dx=\int\left(\frac{A}{1+x}+\frac{B}{2+x}\right)dx\) then A = 1, B = 2.

Q.1 (B) (ii) State whether true or false: If \(\int\frac{x}{(1+x)(2+x)}\,dx=\int\left(\frac{A}{1+x}+\frac{B}{2+x}\right)dx\) then A = 1, B = 2.

Doubtly Asked 28 Oct 2026 Board exam · March 2026 hsc 12th Save WhatsApp Report

Best answer

Answer: False

\(x=A(2+x)+B(1+x)\). Put \(x=-1\): \(-1=A(1)\Rightarrow A=-1\). Put \(x=-2\): \(-2=B(-1)\Rightarrow B=2\). So \(A=-1,\ B=2\), not \(A=1\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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