Answer:
0.7048
Step-by-step explanation:
∫₂⁴ 1 / (x − 1)² dx
n = 4, so we divide the interval into 4 regions. The width of the regions is:
(4 − 2) / 4 = 0.5
So the intervals are (2, 2.5), (2.5, 3), (3, 3.5) and (3.5, 4).
Evaluate f(x) at the ends of each interval.
f(2) = 1
f(2.5) = 4/9
f(3) = 1/4
f(3.5) = 4/25
f(4) = 1/9
Find the area of each trapezoid:
A₁ = ½ (2.5 − 2) (1 + 4/9) = 13/36
A₂ = ½ (3 − 2.5) (4/9 + 1/4) = 25/144
A₃ = ½ (3.5 − 3) (1/4 + 4/25) = 41/400
A₄ = ½ (4 − 3.5) (4/25 + 1/9) = 61/900
So the total approximate area is:
A = 0.705
Closest answer is 0.7048.
