It is given that $$$\int_{0}^{a}\left(\frac{4}{2 x+1}+8 x\right) \mathrm{d} x=10$$$, where $$$a$$$ is a positive constant. Use an iterative formula, based on the equation in part (a), to find the value of $$$a$$$ correct to 4 significant figures. Give the result of each iteration to 6 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_22 Year：2020 Question No：7(c)

Answer:

Use iteration process correctly at least once
Obtain final answer $1.358$
Show sufficient iterations to 6 sf to justify answer or show a sign change in the interval $[1.3575,1.3585]$

Knowledge points:

2.6.3 understand how a given simple iterative formula of the form relates to the equation being solved, and use a given iteration, or an iteration based on a given rearrangement of an equation, to determine a root to a prescribed degree of accuracy. (Knowledge of the condition for convergence is not included, but an understanding that an iteration may fail to converge is expected.)

Answer:

Knowledge points:

Solution:

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