The diagram shows the curve with equation $$\(y=\frac{x-2}{x^{2}+8}\)$$. The shaded region is bounded by the curve and the lines $$\(x=14\)$$ and $$\(y=0\)$$. Use the trapezium rule with three intervals to find an approximation to the area of the shaded region. Give the answer correct to 2 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_22 Year：2020 Question No：4(b)
Answer:
Use \(y\) values \((0), \frac{4}{44}, \frac{8}{108}, \frac{12}{204}\) or decimal equivalents
Use correct formula, or equivalent, with \(h=4\)
Obtain \(2\left(0+2 \times \frac{4}{44}+2 \times \frac{8}{108}+\frac{12}{204}\right)\) or equivalent and hence \(0.78\)
Use correct formula, or equivalent, with \(h=4\)
Obtain \(2\left(0+2 \times \frac{4}{44}+2 \times \frac{8}{108}+\frac{12}{204}\right)\) or equivalent and hence \(0.78\)
Knowledge points:
2.5.3 understand and use the trapezium rule to estimate the value of a definite integral. (Including use of sketch graphs in simple cases to determine whether the trapezium rule gives an over estimate or an under-estimate.)
Solution:
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