Question

use the trapezoid rule with n=3 to approximate the area under y=x^2 from x=1 to x=4.

Answer 1

Divide the interval [1,4] into 3 intervals each of length 1
Then make the table
x | 1 2 3 4
y | 1 4 9 16
Then by trapezoid rule

(1/2)*1(1+2*2+2*3+4) =(1/2)(1+4+6+4)=15/2.