Question

Use the Trapezoid Rule of n = 4 to approximate

Answer 1

Answer:

The integral is 0.5090

Step-by-step explanation:

Given:

`\begin{gathered} f(x)=(1)/((x-1)^2) \\ \\ [a,b]=[2,3] \\ n=4 \end{gathered}`

We have:

`\Delta x=(b-a)/(4)=(3-2)/(4)=(1)/(4)`

The starting point is a = 2 and end point is b = 3. Then

`\begin{gathered} x_0=2 \\ \\ x_1=2+(1)/(4)=(9)/(4) \\ \\ x_2=(9)/(4)+(1)/(4)=(10)/(4)=(5)/(2) \\ \\ x_3=(11)/(4) \\ \\ x_4=(12)/(4)=3 \end{gathered}`

Finally, we have the integral as:

`\begin{gathered} I=(\Delta)/(2)[f(x_0)+2f(x_1)+2f(x_2)+2f(x_3)+f(x_4)] \\ \\ =(1)/(8)[f(2)+2f((9)/(4))+2((5)/(2))+2f((11)/(4))+f(3)] \\ \\ =(1)/(8)[1+(32)/(25)+(8)/(9)+(32)/(49)+(1)/(4)] \\ \\ =0.5090 \end{gathered}`