Mathematics · JEE | INTEGRALS

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The integral \( \int \frac{dx}{x^2 + a^2} \) equals \( \frac{1}{a} \tan^{-1}(\frac{x}{a}) + C \). Reason (R): By substituting \( x = a \tan\theta \), the differential \( dx = a \sec^2\theta \, d\theta \), which simplifies the integrand to \( \frac{1}{a} \int d\theta \). In the light of the above statements, choose the correct answer from the options given below:

1. A
   Both (A) and (R) are true and (R) is the correct explanation of (A).
2. B
   Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
3. C
   (A) is true but (R) is false.
4. D
   (A) is false but (R) is true.