Question

need help. please amswer #3 and 4

• The Midpoint Rule. Trapezoidal Rule. • Simpson's Rule. 2. Using n = 4, approximate the value of وت using all three rules. 3. Using n = 4, approximate the value of 1 l, dc 1+r2 using all three rules. 4. Using n = 4, approximate the value of L using all three rules.

Answer 1

we have 's the che, n=4 o a-o b=1 Divide the interval [0, 1] into An= b-a - 10 - 144 n=4 Subintervals of length An=144 1332 64 65 2-0,t's feletu) = f( 0+)=f(b) + FC Painting) = f( $ ) - 4( 3 ) it 32 73 f(*e*23) = 44*) - 4(3) 64 HD 89 flugt mly) - HE!) = f(3) = t(72)2 - 113 By Mid point rule, S fcm) dx = Am [ +(*otr.) + f("unt mg) + 4%*3) f(thiy tomony] [ a[monthnel) + (mitm2) + f(*a *m3) + f(uly tyly)] 64 + -dn- An Itu? 64 +64 +64 +64 65 73 89 113 - 0.786100 Midpoint rule :0.786700

we have a=0; f(0) = f(no) = f(0) = 1 HO f(1) = f( 4 ) = 16 17 HG) 4 f(2)= f ( ) = H() 2 - 5 f(3) = f( 3 ) = f(M4) = f(1) = 1 to2 = 1 - 16 H 25 ㅗ By brapezoidal rule. "Sfm du = AM [ f(Mo) +2 f(M) + 2 f(M2)t +2 f(404)+fen)] lowe do some [(MB) ta-f(mv) + 2 f(l) +24(43) + f(44] 16 ( 1+ 2(14)+2(3)+265)+] = 1/2 [ 14 3 2 1 + 2 + 32 + - 2 ' s = 0.78249411 Trapezoidal rule : 0.7827941 By Simpson's rule 2 dn = s flu) dn - A [ f(-x)+ 4f(mv) + 2 f(12) + +2f (ne) +44(mnt) + f(ur)] A ( f(Mo) +44(MI) + 2 fm2) + 44(43) + f(my)] o [+ 4C4%)+(4+4%)+] (+ + Hu2 25

- 0.78539215 simpson's rule 0.785392 .. Midpoint gule : 0.78670 0 Trapezoidal rule : 0.7827941 simpson's gule : 0.785392