Question

(a) Estimate the area under the graph of f(x) = 4 + 4x2 from x = -1 to x = 2 using three rectangles and right endpoints. R3 = 32 Then improve your estimate by using six rectangles. RG :- 27.5 Sketch the curve and the approximating rectangles for R3. у 20 у 20 15 15 10 10 O-1 2 у у 20 20 15 15 10 10 5 -1 1 2 1 2

Answer 1

the kg and indoor anyximatic@gepreprogetto R6 Egrlich Ro 20 20 15 15 v 10 10 5 5 -1 -0.5 0.5 1 1.5 2 O-1 -0.5 0.5 1 1.5 2 20 20 15 15 10 10- 5 -0.5 0.5 1 1.5 2 O-1 -0.5 0.5 1 1.5 2 Ang (b) Repeat part (a) using left endpoints. L3 - 16 Sketch the curve and the approximating rectangles for L3. Y 20 20 4 + 902 So, 49 = 2-(-1) 15 15 3 = 10- 10- fon) = [[1, 2 do=-1, 2,= 0, d2 = 1, &z=2 * 13 = An. s from) + fra) + fon) + from t fram = '{ fos + f(0) + freu) O-1 20 20 15 15- = 20 10- 10- 5 1=0.5 2 O-1 Sketch the curve and the approximating rectangles for M6- 20 20 1 15 15 = 10 10 Again. An= 2-(-) 6 So, 2. - -1, 2, = -0.5, 2,= 0, dl2 = 0.5,14 = 1 715 = 15, a = 2 An{ ftm.) + from.) + flac) + flam) + fon) + fros) f(1) + fros) + fro) + f(os) + fu + -f(is)] Lo 5 O-1 -0.5 0.5 1 1.5 -0.5 0.5 1 1.5 20 20 15- 15 10 10 = 21.5 Ary -0.5 0.5 O-1 2 1.5 -1 -0.5 0.5 1.5