Question

(1 point) In this problem you will calculate the area between f(x) = x2 and the x-axis over the interval [3,12] using a limit of right-endpoint Riemann sums: Area = lim ( f(xxAx bir (3 forwar). Express the following quantities in terms of n, the number of rectangles in the Riemann sum, and k, the index for the rectangles in the Riemann sum. a. We start by subdividing [3, 12) into n equal width subintervals [x0, x1], [x1, x2),..., [Xn-1, x, each of width Ax. Express the width of each subinterval Ax in terms of the number of subintervals n. Ax = b. Find the right endpoints X1, X2, X3 of the first, second, and third subintervals [x0, x1], [x1, x2], [X2, X3] and express your answers in terms of n. X1, X2, X3 = (Enter a comma separated list.) c. Find a general expression for the right endpoint Xk of the kth subinterval [Xk-1, xx], where 1 sk <n. Express your answer in terms of k and n. Xx = d. Find f(x) in terms of k and n. f(x) = e. Find f (xx)Ax in terms of k and n. f(x)Ax =

Answer 1

a[3122 Giuen foo = 32 소 a=3 be 12 ba = 02 - 3 مااد AC - 9. 1 b) xit Da Hese 3t 34요 n (3가 U2 3+ 18 27 a = (3+용)+용 = 3t Hen e 42 5 6t3 3+18 3427 n 34명 - 으 라 9k d) A= gk2 5부) (3+) 3 (0 focedy n. ) E flak) sx 9 2 (3+k) K지 K= ss 도옭 (9t약 +81k2 ) 1) n2 8 + Efrak) dx 92 541 ) + +8 8 2 려 9) lie ( 227 ) = 5547