Question

trapezoidal rule, simpson's rule or the midpoint rule should be used. I figured out n=147 but using these rules will take a really long time.

b) Estimate S, 3x4 – 1 dx to within .01, using one of the error estimates.

Answer 1

K (b-a75 180n4 K-sup 1 flexes xclub The error bound for Simpson't Rule is Esl < Taking b=3, A=1 f(x)= 3x1, we have flex) = 12x3, f" (X) = 36x² , &" (x) = 72X, f (x) = 72 18'N(x) 1572 k=72. Tak) ng K (6-0) < 0.01 72 x(341) 0.01 18on4 4X2 <nu nu> 128 an"> 1280 loxoool Taking n=6, 64 = 1296>1280, Take n=6 haba = 3-1 = 3 4 ,5 Loox ny co.o jo 0.1 f(1) = 2, H4)= 8.48148), f()= 22.148115 & (2) = 47, (B) = $(7) = 87.925 926 , 8(%) = 150.703704 f(3) = 242 Sea') dx = 180 +43()+2f($) + 4f() +28(3) + 4 F(83) + f(3)] = [2 + 4 ( 8.48148) +47+1561703704 + 2 ( 22.148115 + 87.925926) + 242] = 1288.888822 143« 2098691 143. 2099 Actual value of SB x L 1 )dx= 3 x 5 x 73 = 2.169-15) - (3-1) = 3 x 242 - 2 = 143.2 The emoy = 1143.2 - 143.20991 = 0.0099 <0.01 5