Improper integrals by numerical methods Use the Trapezoid Rule (Section 7.6) to approximate with R =2, 4, and 8. For each value of R, take n = 4, 8, 16, and 32, and compare approximations with successive values of n. Use these approximations to approximate .

Solution:-

Step1

Given that

Use the Trapezoid Rule (Section 7.6) to approximate with R =2, 4, and 8. For each value of R, take n = 4, 8, 16, and 32, . Use these approximations to approximate .

Step2

To find

compare approximations with successive values of n.

Step3

N=4 and R=2

Using trapezoidal rule

Divide interval [0,2] into n=4 subintervals of length

a=0,

f(

2f(

2f(

2f(

f(

Finally , just sum up above values and multiply by

=

=

Step4

N=8 and R=4

Using trapezoidal rule

Divide interval [0,4] into n=8 subintervals of length

a=0,

f(

2f(

2f(

2f(

2f(

2f(

2f(

2f(

f(

Finally , just sum up above values and multiply by

=

=0.886227

Step5

N=16 and R=8

Using trapezoidal rule

Divide interval [0,8] into n=16 subintervals of length

a=0,

f(

2f(

2f(

2f(

.

.

.

.

2f(

f(

Finally , just sum up above values and multiply by

=

=0.886227