Question

estimaye error from trapezoidal rule & simpson

Estimate the error from the trapezoidal role and Simpson's rule when finding an approximation Soux dx with 4 equally spaced subintervals [0, 1]

Answer 1

І s sx dx O b = 1 Here ns4 f(x) = 5x error due to Now, The sule trapezoidal is given by Egle M₂ (b-a) 12n2 where M₂ Maximum value of lf" (x) in the interval [0, +7 f(x) = x f (x) - 1 2 x ava f"+*) = x $12 ie, f (x)= 1 4 x 3/2 .. fhios 4x o 1 f(1) = 4x1 Signature

M IE, 1 = - 4 (1-0)3 1 2 × (492 - 12x16 4 1 768 -0.0013 error Again, The due to simpson's Rule is given by Esl & My Cb-ass 1804 where. My s maximum value of If "(2471 in the interval co 17 oor f(x) sx f'(x) - 25 flat f"(x) 4x3½ 3 8 x 512 Is f (x) = 16 x 7/2 2 Stature

15 16xo 15 168f IS 16 15 . My i lesla -16 (1-095 180 × (49 -18 16x 180 x 256 12 1 49152 0.00002