Question

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)

1/2

0

10 sin(x²) dx, n = 4

Answer 1

2lo # Strong ft ju sinfire", da, nah hers fees a loSix (222). Tropezadel Rule Jhy dx = she llot yn + 2(yit Yat Yzt- Yare) ho 19.4 f(3) t (3/8) [ Since Sin() + sin(5)*+ 27 Sim( $) + Sik ( **() + sin(3)")] hers Dx= You → Ax=1 -امد 1o Sin (20²) du = Dx 2 2. o LO 2 8x2 1/16 3/16 5/16 1/16 0.4280642 0.428064 Answer Using Midpoints Rule Miel points T 1 0 1/8 2/8 3/8 4/8 = 1/2 Dove [ 444) + f(%) + free)+ 1977)] 10x x Anz27962 0+32 8117 fr = 0.4101472

1/2 0.410147) Inseen Uusing Simpson's Rule & s lo sin (x²) the Spel fro) + f()+4(f(8) + f[]))+2f(1)] Ixlox0.9974036 883 =/0.415585 Answer
Answer: Trapezoidal rule = 0.428064

Mid point rule = 0.410147

Simpson rule = 0.415585

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