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. Show that $$$a=\sqrt{2.5-0.5 \ln (2 a+1)}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_23 Year：2020 Question No：7(a)

Answer:

Integrate to obtain the form $k_{1} \ln (2 x+1)+k_{2} x^{2}$
Obtain correct $2 \ln (2 x+1)+4 x^{2}$
Use limits correctly and attempt rearrangement
Confirm $a=\sqrt{2.5-0.5 \ln (2 a+1)} \quad \mathrm{AG}$

Knowledge points:

2.5.1 extend the idea of 'reverse differentiation' to include the integration of (Knowledge of the general method of integration by substitution is not required.)

Answer:

Knowledge points:

Solution:

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