1. Express the following limits as a definite integral: (a) lim 19–1 xịIn(1 + xi;?))Ax (2,6]...
Express the limit as a definite integral on the given interval. lim n00 1 = 1 X; In(1 + x2) Ax, [2, 4] SI dx
Question 4 4.1 Express the limit as a definite integral on the given integral: 1-x} Ax , [2,6] lim Σ=1 a. (2 Marks) n->00 4+x} lim (?-1 - Ax ,[1,3] (xi) - 4 b. (2 Marks) n->00 4.2 Evaluate the following expressions. Show your calculations. $=1(2p – p2) b. En-o sin a. (2 Marks) пп (2 Marks) 2 C. 2m +2 53 Lm=1 3 (2 Marks) [Sub Total 10 Marks]
7. Express the limits lim sin(x: Aras a definite integral on the interval [0.2) and then evaluate the integral
A. Express the limit as a definite integral on the given interval. B. Use the form of the definition of the integral to evaluate the integral. n Š lim n-> Xi Ax, [1, 3] (xi +13 * 2 i=1 3 6 (2x - x2) dx
Express the following limit as a definite integral. n 1 lim P10 k=1 -Axk where P is a partition of [3,5] 5 The definite integral is si dx. 3
(1 point) The limit lim /2x + (x)?Ax 11 can be expressed as a definite integral on the interval [1, 8] of the form $(x) dx Determine a, b, and f(x). a = b= f(x) =
n Express the limit lim (3 cos” (272,-) + 8)Ac; over (2,6) as an integral. 12 00 i=1 Provide a, b and f(x) in the expression [ f(e)dr. a = b f()
Express the following limit as a definite integral: 22 3i lim n-+00 2522 n2 1 n2 i=1
8. Express the limit as a definite integral on the given iterval. lim :0;)2 + 44.2 on (1.3) (a) Si 7244dx (b) S dx (e) tada (d) $3 2274 d.
5. (-/1 Points] DETAILS SCALC8 4.2.503.XP. Express the limit as a definite integral on the given interval. n lim 3x;* + (x;*)2 Ax, [1,4] i = 1 dx