Question

Can you solve all the parts please?

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 1/2 dt, n = 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

Answer 1

& Calculate 112 dt m=8 7 sim le 112) (a) The trupe zuidul sule stakes that (916) + f/4m) + 2 +14 27414) b AL f(t) de 0 where: b-a At = we have that b= /2 , m = 8 10, aco, & f(t) = 7 sim lett) At = 1/2 = 8 n=8 there five 1/16 into Divide the interval interval [0, 1] subintervunts of length At=1/16 with the following andpunts 1 as to so, t = Vic, te = 24 tz = 3 16 • tu 4/16, ts=5/16 to = 6/16, tz ale to 8 16 t=b 2

then from 2/7 s'i sin le ur) de setembre 1 t/eo) + tle) + až raj. 101.2 3627145 ܐܐ X 32 3.16363348 SI ( 6 ) midpoint rute たっ mol @ f(t) dt f (ti + tits Σ ? At ) J-O a where At - b-a have that we stu 6=72, aco, then from ② sinceta) de a tel(; + kics) ] f 217 7 X T 50.62297714 16 a 3.16393607

is (c). The simpson's rule f(t) dt st + J'rer 1-/ ittelt 3nt ("718+ (0715 0-F ? At ndz -1 &W 2 + f (4₂) -! but all all required 4 sinlet12) de 1/2 + f(+8)+4? Interlt (477) 3 + 2 2 16 3 l 151.86408181) = 3.16383503 48