Mathematics · JEE | INTEGRALS

Given below are two statements: Statement I: The integral \( \int \sin^2 x \, dx \) can be evaluated directly by applying the trigonometric identity \( \cos 2x = 1 - 2\sin^2 x \). Statement II: Integration by substitution requires the derivative of the substituted function to appear as a factor in the integrand. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A
   Both Statement I and Statement II are correct.
2. B
   Both Statement I and Statement II are incorrect.
3. C
   Statement I is correct but Statement II is incorrect.
4. D
   Statement I is incorrect but Statement II is correct.