Integral Calculus HELP

Question

Approximate the value of the given integral by use of the trapezoidal​ rule, using the given value of n.

Integral from 2 to 3 6/7x dx n = 2

Answer 1

f(2) = 12/7

f(2.5) = 15/7

f(3) = 18/7

Area of the trapezoid:

area of the rectangle + area of the right triangle

= deltaX* min(f) + (1/2)(deltaX)(deltaY)

So from 2 to 2.5:

(1/2)((12/7) + (1/2)(1/2)(3/7)

12/14 + 3/28 = (24+3)/28 = 27/28

From 2.5 to 3:

(1/2)(15/7) + (1/2)(1/2)(3/7)

15/14 + 3/28 =

(30+3)/28 = 33/28

total area = (27+33)/28 = 60/28 = 30/14 = 15/7

This makes sense... area above the curve cancels the

area below the curve