Trapezoidal rule 3

Evaluate

By using Trapezoidal rule

Solution:-

h= 10-0/10 = 1

y= f(x) = 1/ 1+ x^2

X            y

0            1

1            0.5

2            0.2

3            0.1

4            0.05882

5            0.03846

6            0.02702

7            0.02

8            0.01538

9            0.01219

10          0.00990

Using Trapezoidal rule

Integration of Y dx = h/2 [ (Y0 + Yn) + 2(Y1 + Y2+ .......... Y(n-1) ]

=> 1/2[ (1+0.00990) + 2(0.5+ 0.2 + 0.1 + 0.05882+0.03846 + 0.02702 + 0.02+ 0.01538 + 0.01219) ]

=> 0.5 [ 1.00990 + 2× 0.94485]

=> 0.5 [ 1.00990 + 1.88971 ]

=>  1.449805