Edexcel IAL WMA12/01/P2/Oct 2021/Q3 (Logarithms, The Trapezium Rule)
Figure 1 shows a sketch of part of the curve with equation
The region R, shown shaded in Figure 1, is bounded by the curve, the line with equation x = 2, the x-axis and the line with equation x = 14
Using the trapezium rule with four strips of equal width,
show that the area of R is approximately 10.10
(3)
Explain how the trapezium rule could be used to obtain a more accurate estimate for the area of R.
(1)
Using the answer to part (a) and making your method clear, estimate the value of
(4)
SOLUTION
a- Using Trapezium Rule to estimate the shaded area below the curve
(First, divide the area under the curve into 4 equal trapezium strips as given in the question. To know the x values, let us first find the value of h or the width of each trapezium strip.)
Let us now construct the table of x and y values. Picking the x values at the difference of 3 as h=3, and finding their respoective values of y which are the parallel lengths of the trapezium strips.
x | 2 | 5 | 8 | 11 | 14 |
Now, applying the trapezium formula from the flash card above.
b- By dividing the area under the curve into more trapezium strips.
c- i-
Substituting the value of
c-ii-
Remember,
Applying the power rule on
Substituting the value of
Solving the rest of the integration.
Applying the limits.
