Use the trapezium rule with three intervals to find an approximation to $$$\int_{1}^{4} \frac{6}{1+\sqrt{x}} \mathrm{~d} x$$$. Give your answer correct to 5 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_21 Year：2021 Question No：6(a)

Answer:

Use $y$-values $3, \quad \frac{6}{1+\sqrt{2}}, \quad \frac{6}{1+\sqrt{3}}, 2$
or $3,6 \sqrt{2}-6,3 \sqrt{3}-3,2$
or $3,2.4853 \ldots, \quad 2.19615 \ldots, \quad 2$
Use correct formula, OE, with $h=1$
Obtain $7.1814$

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.)

Answer:

Knowledge points:

Solution:

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