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1 1 of 19 (1 complete) a) Approximate the area under graph (a) of t(x)-1/x over

ID: 2890108 • Letter: 1

Question

1 1 of 19 (1 complete) a) Approximate the area under graph (a) of t(x)-1/x over the interval [2,10] by computing the area of each rectangle to four decimal places and then adding b) Approximate the area under graph (b) of 10) 1/x over the inferval 12, 10] by computing the area of each rectangle to four decimal places and then adding The area urder graph (a) is approximately (Round to four decimal places as needed.) 0.125 The area under graph (b) is approximately (Round to four decimal places as needed.) 10 0.1 3 4 56 7 8 9 10

Explanation / Answer

a)

Height of first rectangle=f(2)=0.25 => Area=0.25*2=0.5

Height of second rectangle=f(4)=0.125/2 => Area=0.125/2*2=0.125

Height of third rectangle=f(6)=0.25/9 => Area=0.25/9*2=0.5/9=0.0555

Height of fourth rectangle=f(8)=0.25/16 => Area=0.25/16*2=0.5/16=0.03125

Total area=0.5+0.125+0.0555+0.03125=0.71175

b)

Height of first rectangle=f(2)=0.25 => Area=0.25*1=0.25

Height of second rectangle=f(3)=0.25/4 => Area=0.25/4*1=0.0625

Height of third rectangle=f(4)=0.25/9 => Area=0.25/9*1=0.25/9=0.0277

Height of fourth rectangle=f(5)=0.25/16 => Area=0.25/16*1=0.125/8=0.015625

Height of fourth rectangle=f(6)=0.25/25 => Area=0.25/25*1=0.01

Height of fourth rectangle=f(7)=0.25/36 => Area=0.25/36*1=0.00694

Height of fourth rectangle=f(8)=0.25/49 => Area=0.25/49*1=0.0051

Height of fourth rectangle=f(6)=0.25/81 => Area=0.25/81*1=0.00308

Total area=0.3810