Answer:
Part (a)
Given:
Trapezium Rule
Calculate the width of each strip (h).
Given:
Create a table with the x and y values:
Put all the values into the formula:
Part (b)
The exact area as a decimal is
. Therefore, the estimated answer of 8.72 is an overestimate.
Part (c)
Answer to (a) = 8.72
To find the maximum possible error:
- Identify the last non-zero digit to the right of the decimal point → 2
- The precision of the number is the place value: 0.01
- Divide the precision by 2
Therefore, the maximum possible error for 8.72 is 0.005.
Part (d)
Trapezoid Error formula
Calculate the second derivative:
Input the values into the formula: