Match Column I to Column II. (A) ∫ 4 10 ⌊ x 2 − 28 x + 196 ⌋ + ⌊ x 2 ⌋ ⌊ x 2 ⌋ d x . (B) ∫ − 1 2 ∣ x ∣/ x d x . (C) lim n → ∞ ( 1 99 + 2 99 + ⋯ + n 99 ) / n 100 . (D) If 5050 ∫ − 1 1 x 200

Question

Match Column I to Column II. (A) ∫ 4 10 ​ ⌊ x 2 − 28 x + 196 ⌋ + ⌊ x 2 ⌋ ⌊ x 2 ⌋ ​ d x . (B) ∫ − 1 2 ​ ∣ x ∣/ x d x . (C) lim n → ∞ ​ ( 1 99 + 2 99 + ⋯ + n 99 ) / n 100 . (D) If 5050 ∫ − 1 1 ​ x 200 ​ d x = 1/ α , find α . Column II: (P) 1/100, (Q) 3, (R) 1/3, (S) 1.

TestHub · Accepted Answer

For (A), pair x with 14 − x ; the two fractions add to 1, so the integral is 3 . (B) is − 1 + 2 = 1 . (C) is the Riemann integral ∫ 0 1 ​ t 99 d t = 1/100 . (D) equals 5050 ⋅ 2/101 = 100 = 1/ α , so α = 1/100 .

Mathematics - Definite Integration Question with Solution | TestHub

Options:

Doubts & Discussion