Maths · Calculus · chapter 7 of 13
Class 12 Maths Chapter 7: Integrals Assertion-reason questions with answers
2 assertion-reason questions on Integrals, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.
Question 1
Assertion (A): ∫ dxx = log |x| + C for x ≠ 0. Reason (R): ddx log |x| = 1x both for x > 0 and for x < 0.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.
For x < 0, log |x| = log (−x) has derivative −1−x = 1x. R is true and is exactly why log |x| is an anti derivative of 1x on both sides of 0, so A follows from R.
Question 2
Assertion (A): ∫−11 x |x| dx = 0. Reason (R): ∫−aa f(x) dx = 2 ∫0a f(x) dx when f is an even function.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.
x |x| is odd, so A is true by P₇ (ii). R is P₇ (i), also true, but it concerns even functions and does not explain A.
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