numerical mathod course

formula sheet for solvinig the orobla

please solve it manually

Problem \#4: Use Romberg integration to evaluate 021+x2exdx to an accuracy of s0,a=1xdx=lnx+Cx=0sinax+bdx=a1cosax+b+ccos(ax+b)dx=a1sin(ax+b)+clnxdx=xlnxx+Cedx=aea+Cxd=7dx=a2e2xax1+Ca+bx2dx=ab1tan1aabx+C Trapezoidal Rule: I=(ba)2f(a)+f(b)Et=121f()(ba)3h=nbaI=2h[f(x0)+2l=1n1f(xj)+f(xn)]Frror12(ha)2max12f(x)(OnelatervalCase)R(n,0)=21R(n1,0)+h[k=12(1)f(a+(2k1)h)]I1516Im151IlI6364Im631IlR(n,m)=R(n,m1)+4m11[R(n,m1)R(n1,m1)]forn1,m1