∫ 0 3 2 + x 2 d x =

Question

∫ 0 3 2 + x 2 d x =, lim n → ∞ 1 n 2 n + 1 2 + 2 2 + … + 3 n 2 n 2, lim n → ∞ 1 n 3 n + 1 2 + 2 2 + … + 6 n 2 n 2, lim n → ∞ 1 n 6 n + 1 2 + 2 2 + … + 9 n 2 n 2, lim n → ∞ 1 n 3 n + 1 2 + 2 2 + … + 3 n 2 n 2

MARKS App · Accepted Answer

Let 2 + x 2 = f ( x ) ⇒ ∫ 0 3 2 + x 2 d x = ∫ 0 3 f x d x Now, ∫ 0 3 f x d x = lim n → ∞ 1 n ∑ r = 1 3 n f r n = lim n → ∞ 1 n ∑ r = 1 3 n 2 + r n 2 = lim n → ∞ 1 n 2 × 3 n + 1 2 + 2 2 + 3 2 + … + 3 n 2 n 2 = lim n → ∞ 1 n 6 n + 1 2 + 2 2 + 3 2 + … + 3 n 2 n 2

Search any question & find its solution

Looking for more such questions to practice?