Q.1 (A) (iii) ∫₂⁷√(x)/√(x)+√(9-x) dx= A. 7/2 B. 5/2 C. 7 D. 2

Answer: B. 5/2 Answer: (b) 5/2 Let I=∫₂⁷√(x)/√(x)+√(9-x)dx . Using ∫_a^bf(x)dx=∫_a^bf(a+b-x)dx with a+b=9 : I=∫₂⁷√(9-x)/√(9-x)+√(x)dx . Adding, 2I=∫₂⁷ 1 dx=7-2=5 , so I=5/2 .

\(\int_2^7\frac{\sqrt{x}}{\sqrt{x}+\sqrt{9-x}}\,dx=\)

Q.1 (A) (iii) \(\int_2^7\frac{\sqrt{x}}{\sqrt{x}+\sqrt{9-x}}\,dx=\)

A. \(\frac{7}{2}\)

B. \(\frac{5}{2}\)

C. 7

D. 2

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: B. \(\frac{5}{2}\)

Answer: (b) \(\frac{5}{2}\)

Let \(I=\int_2^7\frac{\sqrt{x}}{\sqrt{x}+\sqrt{9-x}}dx\). Using \(\int_a^bf(x)dx=\int_a^bf(a+b-x)dx\) with \(a+b=9\): \(I=\int_2^7\frac{\sqrt{9-x}}{\sqrt{9-x}+\sqrt{x}}dx\).

Adding, \(2I=\int_2^7 1\,dx=7-2=5\), so \(I=\frac{5}{2}\).

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

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\(\int_2^7\frac{\sqrt{x}}{\sqrt{x}+\sqrt{9-x}}\,dx=\)

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