Question

Consider the following. (a) By reading values from the given graph of f, use five rectangles to find a lower estimate for the area under the given graph off from x = 0 to x = 10. (Round your answer to one decimal place.) 10 Sketch the rectangles that our USA By reading values from the given graph of f, use five rectangles to find an upper estimate for the area under the given graph of Ffrom x = 0 to x = 10. (Round your answer to one decimal place.) Sketch the rectangles that you LISA (1) Find new estimates using ten rectangles in each case. (Round your answers to one decimal place.) (lower estimate) (upper estimate)

Answer 1

Lower Area Left endpoint gives upper estimate. Area = AX (FCO) + F(2)+54) +fm+F(81) ~ 2(6+ 6+3 7+2-1+13+0.8) Area 27-8 for upper estimate Right endpoint gives lower estimate Area AX (F(2) + f(4) + f(6) + f(8)+ f(10)) ~2( 3.7.+2-1+1-3 +0-8+0-5) :. Area 16-8 for lower estimate Upper Area b. Given n=10 rectangles, [0, 0] Ar= 10-0= 1 11 ..LA Are Sub intervals are:[0, 1] [1, 2] [2, 3] [3, 4] 14,5],[5,6],[6.73 [7,8] [8,43 (9,1] from the graph, f(0) = 6, f(1) = 4.7 f(2)=3-7, f(3) = 2.9, F(4) - 2-1, $(5) = 1-8, F(G) = 1-3, F(7)= 1F(8) = 0.85(9) = 0-5, (10)=0-5

) Lower estimate = (Right end point) fu) decreasing Area = AX ( f(0)+F(2)+ $(3)+FCU+ f(s)+F(6)+F(7) + F() + f(9) + f(10) =1-(4+7+ 3-7+2.9+2-1+1-8 +1+3+1+0-8 to-Gto.5) 19.4 Area & 19-41 for lower estimate n=10 Upper estimate (Left endpoint) ? Area = on (560)+F(1) +$2)+F(3)+F(14)+ f(s) + F(6) +F(7) +F(8) +519)) =10(6+4.7 + 3-7+2.9+2-1+1-8+1-3+1 +0.8 to 6) = 24-9 Lo Ariea ? 24.9 four upper estimele n=10