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Class 12 Integrals · Assertion Reason1 Marksintegration_properties

Class 12 Maths · Integrals · Assertion Reason #30

Assertion: If f′(x)=x+1/(1+x²) and f(0)=0, then f(x)=x²/2+arctan x. Reason: For real n≠−1 on a real interval where the powers and derivative are defined, \(\int x^n dx=x^{n+1}/(n+1)+C\).

✅ Step-by-Step Solution

Final Answer: Option (B): Both A and R are true, but R does not correctly explain A.
  1. Integrate the sum to x²/2+arctan x+C and use f(0)=0. R alone only treats the polynomial part, not the rational term or initial condition.

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