Using Simpson's area rule, calculate the area of earth to be excavated given the integral:
b
f(x)dx
a
Where a=1, b=5, and f(x)=1/x^2
do this using 8 intervals
5-1/8 = 0.5
x 2/√x
1 2
1.5 1.633
2 1.414
2.5 1.265
3 1.155
3.5 1.069
4 1
4.5 0.943
5 0.894
1.633 + 1.265 + 1.069 + 0.943 x 4 = 19.64
2 + 0.894 =2.894
1.414+ 1.155 + 1 =3.569 x2 =7.138
1/3 x 0.5 [2.894 + 9.64 + 7.138] = 8.701 to 3dp
Would this be the right working out/method and answer.
b
f(x)dx
a
Where a=1, b=5, and f(x)=1/x^2
do this using 8 intervals
5-1/8 = 0.5
x 2/√x
1 2
1.5 1.633
2 1.414
2.5 1.265
3 1.155
3.5 1.069
4 1
4.5 0.943
5 0.894
1.633 + 1.265 + 1.069 + 0.943 x 4 = 19.64
2 + 0.894 =2.894
1.414+ 1.155 + 1 =3.569 x2 =7.138
1/3 x 0.5 [2.894 + 9.64 + 7.138] = 8.701 to 3dp
Would this be the right working out/method and answer.