Question

Using (i)Trapezoidal rule (ii) Simpson’s 1/3 rule (iii) Simpson’s1/3 rule, solve x 0.0 0.1 0.2 0.3 0.4 f(x) 1.0000 0.9975 0.9900 0.9776 0.8604​

Answer 1

Answer:

x 0 0.1 0.2 0.3 0.4

y 1 0.9975 0.99 0.9776 0.8604

Using Simpsons

1

3

Rule

∫ydx=

h

3

[(y0+y4)+4(y1+y3)+2(y2)]

∫ydx=

0.1

3

[(1+0.8604)+4×(0.9975+0.9776)+2×(0.99)]

∫ydx=

0.1

3

[(1+0.8604)+4×(1.9751)+2×(0.99)]

∫ydx=0.39136

Solution by Simpson's

1

3

Rule is 0.39136