Use Simpson's rule to estimate the volume from the given cross sectional areas. x(cm)
-1) 0
-0) 5
0) 0
0) 5
1) 0
A(x) (cm²)
1) 4
1) 5
2) 0
2) 5
2) 6

Question

Use Simpson's rule to estimate the volume from the given cross sectional areas. x(cm) -1)0 -0)5 0)0 0)5 1)0 A(x) (cm²) 1)4 1)5 2)0 2)5 2)6 A) 3.3 B) 4.0 C) 12.0 D) 6.0

Quizplus · Accepted Answer

Using Simpson's Rule, we can estimate the volume as follows:

V ≈ ∫[0,2.6] A(x) dx ≈ (2.6-0)/6 [A(0) + 4A(0.5) + 2A(1) + 4A(1.5) + A(2) + A(2.6)]
V ≈ 0.433 [0 + 4(4) + 2(5) + 4(0) + 2.6 + 3.3] ≈ 1.7706 cm^3

Therefore, the best choice is B, 4.0 cm^3.

Use Simpson's Rule to Estimate the Volume from the Given