Simpson's Rule questions.?

Question

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.)

1. y = e^−x^2, 0 ≤ x ≤ 1

2.y = x + sqrt(x), 2 ≤ x ≤ 5

Answer 1

Surface area obtained by rotating the curve about the x - axis : .

1).

The function , where 0 ≤ x ≤ 1.

Surface area obtained by rotating the curve about the x - axis : .

Let,

By Simpson's rule :

Here, n = 10 and .

and

Answer 2

Contd..........

Substitute corresponding values in equation (1).

.

Therefore, surface area obtained by rotating the curve about the x - axis is - 50.11556 sq.units.

Answer 3

Surface area obtained by rotating the curve about the x - axis : .

2).

The function , where 2 ≤ x ≤ 5.

Surface area obtained by rotating the curve about the x - axis : .

Let, .

Answer 4

Contd.......

By Simpson's rule :

Here, n = 10 and .

.

Substitute corresponding values in equation (1).

.

.

Therefore, surface area obtained by rotating the curve about the x - axis is 92.3392 sq.units.