Question

upson's Rule with n=4 #5 (9) Use Simpson's Rule wi intervals to estimate ex-l at 16 Find the exact value - A the error. drant of the integral linpartas) and the =0: #5, Use integration by. Seť Int de #7 (a) Evaluate St sin x cos x dic (6) If g(x) = 5 Je tidt, find g'(x) and g'(o). |#8 use partial fractions to find substitution to evaluate $3x(x-3) dx #0 (a). Find 52 sin o do (6) Find the Riemann sum for 5x²dx with n=3 subintervals § using right endpoints as the sample points. Show all your work for full credit! Submit this piece of paper as well as your solutions, write your name on each ! Duration 2:00-3:40

Answer 1

6) tentat Taking ent as ist fune" and th as and. xent [lines f*dt - Sant lent) [tdt) d ]; fent-sifat punt - Jatli & ent- eli (es. ene-el) - ( 112-) +) { swansondu sinnt? & casada edt 7 Lit sinarto cesada e de om sine I cim² x cos nda Also, sino =0 and sim II l a a So, we have stat glu svt tidt 222 glu) = (vrem-+1) .(2x) - Text1 d. L-a) By using Fundamental theorum of Integral Calculus) & g'(x)= (Jun?+1) (2) - Ja²+1 (-1) alu) = 2/4n²+1+2+1 and g'(o)= 250 + V g'lo) = 3

Sau(n²3)" du net x²-3 = t For n=1, 1-3 = -2 endndt & ndne ldt ; n = 2, 4-3=1 n one 2 . 3. tat - 3 Sthat since e this even fl-t) = fcts function for f(t) = 44. hence it'at - 25+' 4t curing properties of definite integral 2IT yine dobro 09" 1-31-0 Now, the general formula to find integral using right end points is 2 (b-a) f(ME) where #ni) = (1 + 1 1 2 te - 24-643) . , (+ ++) {(n+ nhanh) + (n+1)(2xJ ] fere n=3, Thus we have (3+ 3 4 + 34.7) = 21 .
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