Question

The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of

Answer 1

- The formula for finding the integral of a function using the trapezoidal rule is:

`A=(\Delta x_1)/(2)[f(x_0)+f(x_1)]+(\Delta x_2)/(2)[f(x_1)+f(x_2)]+...`

- Applying the formula, we have:

`\begin{gathered} \Delta x_1=1.1-1=0.1,\Delta x_2=1.2-1.1=0.1,\Delta x_3=1.5-1.2=0.3 \\ \Delta x_4=1.7-1.5=0.2,\Delta x_5=1.9-1.7=0.2,\Delta x_6=2.0-1.9=0.1 \\ \\ f(x_0)=f(1)=1 \\ f(x_1)=f(1.1)=2 \\ f(x_2)=f(1.2)=4 \\ f(x_3)=6 \\ f(x_4)=7 \\ f(x_5)=9 \\ f(x_6)=10 \end{gathered}`

- Thus, we can find the Integral as follows:

`\begin{gathered} A=(0.1)/(2)(2+1)+(0.1)/(2)(4+2)+(0.3)/(2)(6+4)+(0.2)/(2)(7+6)+(0.2)/(2)(9+7)+(0.1)/(2)(9+10) \\ \\ A=(0.3)/(2)+(0.8)/(2)+(3)/(2)+(2.6)/(2)+1.6+(1.9)/(2) \\ \\ A=5.9 \end{gathered}`

Final Answer

The integral is 5.9