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Hetkumar Jagdishkumar PatelOdishMAT266Spring2020Assignment Section6.5 due 02/08/2020 at 11:59pm MST1.(1 point)Given the following integral and value of n, approximatethe following integral using the methods indicated (round youranswers to six decimal places):Z10e-3x2dx,n=4(a) Trapezoidal Rule(b) Midpoint Rule(c) Simpson’s Rule0=0,x1=14,x2=12,x3=34, andx4=1.hf(x0)+2f(x1)+(c) Simpson’s Rule withn=4 isS4=Δx3hf(x0)+4f(x1)+2f(x2)+4f(x3)+f(x4)i.So withf(x) =e-3x2S4=1/43hf(0)+4f(14)+2f(12)+4f(34)+f(1)i=112h1+4e-3/16+2e-3/4+4e-3(9)/16+e-3i≈112h1+3.31612+0.944733+0.739926+0.0497871i≈0.504214•0.505095•0.504213(correct)2.(1 point) A radar gun was used to record the speed ofa runner during the first 5 seconds of a race (see table).UseSimpson’s rule to estimate the distance the runner covered dur-ing those 5 seconds.•40.8751
3.(1 point)Consider the integral approximationT20ofR402e-x4dx.DoesT20overestimate or underestimate the exact value?•A. overestimates•B. underestimatesFind the error bound forT20without calculatingTNusing theresult that