Some values of the function ft e are given in the table bel

Some values of the function f(t) = e-~ are given in the table below. By setting up a Riemann sum using 7 subintervals, find an upper estimate to the definite integral Use your calculator where appropriate, and show all working.

Solution

\\int_{0}^{1} e^(-t^4) a=0 b=1 n=7 h= (b-a)/n=(1-0)/7=1/7 f(t) = e^(-t^4) f(0)= 1 f(0.25)= 0.996101 f(0.5)=0.939413 f(0.6)=0.878447 f(0.7)= 0.786549 f(0.8)=0.663916 f(0.9)= 0.518871 f(1.0)=0.518871 \\int_{0}^{1} e^(-t^4) = h( f(0.25)+f(0.5)+f(0.6)+f(0.7)+f(0.8)+f(0.9)+f(1.0) ) = (1/7) ( 0.996101+ 0.939413+ 0.878447+ 0.786549+ 0.663916+ 0.518871 +0.518871 ) =0.757453 ANSWER