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Class 12 Integrals · Assertion Reason1 Marksintegration_properties

Class 12 Maths · Integrals · Assertion Reason #27

Assertion: \(\int_2^8\frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}}dx=3\). Reason: For continuous f, \(\int_a^b f(x)dx=\int_a^b f(a+b-x)dx\).

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.
  1. Reflection x↦10−x replaces the numerator by √x. Adding the two equal integrals gives 2I=∫₂⁸1dx=6, hence I=3.

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