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Class 12 Maths Chapter 8: Application of Integrals Assertion-reason questions with answers

2 assertion-reason questions on Application of 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): The area of the region bounded by y = −x2, the x-axis and the ordinates x = 0 and x = 3 is 9 square units. Reason (R): If f(x) ≤ 0 on [a, b], the area bounded by y = f(x), the x-axis and the ordinates x = a and x = b is |∫ab f(x) dx|.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

∫03 (−x2) dx = −9; the curve is below the x-axis, so the area is |−9| = 9. R is the rule that gives A.

Question 2
Assertion (A): The area of the region bounded by y = cos x, the x-axis and the ordinates x = 0 and x = π2 is 1 square unit. Reason (R): The curve y = cos x lies below the x-axis for π2 < x < 3π2.
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Answer: (b) Both A and R are true, but R is not the correct explanation of A.

A: ∫0π/2 cos x dx = sin π2 − sin 0 = 1, true. R is true, but it is about an interval the region of A does not reach, so it does not explain A.

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