Use the Trapezoidal Rule with n = 4 to approximate

0.3523
0.7048
0.2456
0.4913

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.

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)