Question

Estimate the error from the trapezoidal rule and Simpson's rule when finding an approximation So væde with 4 equally spaced subintervals of (0,1). to

Answer 1

Solution b a firstly, we shall Calculate the given integral using Simpson's rule Comparing given integral with falls se he b-a f(x) ds, we have and given nay 44 bz1 1 Y we have follows tabee. fa O 50 sz 0.75 dy + 0.25 fe ois 0170710678120.8660254038 TO (12) flag) fely)

Momenty DATE by Imson's aule, we have h [fre. J + q [tag) + for)] + 9 t[ota [o 5+ 0.8660254038 2x [0.707 1067812] t. 1] 0 16 565262648 Actual value sha ولم دا 1 2 312 2 343 = 0.6666666667 Corar tove valve approximate value = 0.010140 40 18 7 b by Trapezoidal rule approximate value o given by I fondo hly taly, ty + 4z) &yu ] where yiz f(x;)

ماتعلم Lo fa (0-5 + 0.7071067812 +0.8660 25 40512) ti 6.84328 30 46 a. error & Actual value approximate value 0.02338362046. The answere's are (a) 0.02338 36 204f (6) 0.010140 40 187