Question

A- Using a numerical integration method of your choice with n ≥ 70, determine the length of the curve, f(x) = -e^x over the interval [4, 8]

B- Redo question A, using an entirely different numerical integration method.

show all the work please

Answer 1

Page ① using a numerical integration method of your choice with no, to determine the length of the cure fex=-e? over the interval [4,8] bi let simpson's rule states that fondan sx fao) tafexes + fox) 3 + 4 fedzat Efenat.+ z(anz) +4feant) & ferno where Ax=b-a here a=4,6=8 and noto we take n=70 for fx--e ox=8-6 2 35 2 35 Biride the interval [4,8] into nato subintervalsoflength $x = with following points 142 144 276 278 35 35 a = 4 142 b=8 35 35

texas-fear-fas=ae Page ① =-54.598150033 4 fea) = 4€ ( 162 (-) = -4035 142 35 =-231.23572637 2fcdg) = zf (144)=-2 144 20 35 = -122.416956605 4F (269) = 4F (78)=46-23s 278 fixto) - 4 foxlog) - 11266.5720314376 Feb) =FESS -e3=- 2980.9579870 Finally from m ② Sedan 2 2 (-54,598150033-231.2356637 -122.416956GOS - 11261.5720314376 9 - 2980. g5798706) s-edas - 2926, 360odo 28 292 but length of curve never negative : length of given runes 2926.3600 unit

of your choice with n 70. Page ③ Given curre is fex = h over the integral interval [4,8] We have to find length of curve using a numerical integration method We know that Length of the curve is given by L=1 / (+ ( x²+ da f (xo firstly find differentiate fex with respect for a fens = die) d dre da f(x) = -e cid = el du 8 L=src-et?ts da 4 rent du

Page x2?^)=1 e + (Tt T+ x n ) un 2x INT-T+xPour + = 7 + Bxer up tott dolets tollerstood + 2 -Vet in 18++ (r-promenlur Inl + L = selesa in Jeets to Anllestill + 8+ 8 T + 1+1+8fur + IT-T+ L=Sedotat enllesti-l invest to resti - Indeets to td td _Inlett- Lu 2926.3688 unit