Complete the table below with the value of y corresponding to x = 1.3, giving your answer to 4 decimal places - Edexcel - A-Level Maths Pure - Question 4 - 2013 - Paper 5

To apply the trapezium rule, we use the formula:

$T = \frac{b - a}{2n} \left( f(a) + 2 \sum_{i=1}^{n-1} f(x_i) + f(b) \right)$

For this case:

• a = 1
• b = 1.5
• n = 5 (since we have 5 intervals)
• f(1) = 0.7071, f(1.1) = 0.7591, f(1.2) = 0.8090, f(1.3) = 0.8572, f(1.4) = 0.9037, f(1.5) = 0.9487

Calculate step-by-step:

1. Calculate the sum of the intermediate values: $\sum_{i=1}^{4} f(x_i) = 0.7591 + 0.8090 + 0.8572 + 0.9037 = 3.3290$

2. Substitute into the trapezium rule formula:

   $T = \frac{1.5 - 1}{2 \times 5} \left( 0.7071 + 2(3.3290) + 0.9487 \right)$ $= \frac{0.5}{10} \left( 0.7071 + 6.6580 + 0.9487 \right)$ $= 0.05 \cdot 7.3138 = 0.36569$

3. Finally, round to three decimal places:

   $\approx 0.366$