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Class 12 Integrals · Assertion Reason1 Marksintegration_properties

Class 12 Maths · Integrals · Assertion Reason #32

Assertion: The convergent improper integral \(\int_0^1 dx/\sqrt{1-x^2}=\pi/2\). Reason: For a>0, \(\int dx/(a^2+x^2)=(1/a)\arctan(x/a)+C\).

✅ Step-by-Step Solution

Final Answer: Option (B): Both A and R are true, but R does not correctly explain A.
  1. Using arcsin x, the limit at the upper endpoint is π/2. R is true but concerns a different integrand.

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