Integral Calculus HELP

Question

Approximate the value of the given integra

(a) Use the trapezoidal​ rule, using

n=4.

​(b) Check by direct integration.

Integral from 0 to 2 3x^2 dx

Answer 1

Using the Trapezoidal Rule, the area is approximately

[1/2 (f(0) + 2f(1/2) + 2f(1) + 2f(3/2) + f(2))]*(1/2)

1/4 (0 + 3/2 + 6 + 27/2 + 12)

= 1/4 (33)

= 33/4 = 8.25

The actual area is ∫₀² 3x^2 dx = x^3 |₀² = 8