$\text { It is given that } \int_{a}^{3 a} \frac{2}{2 x-5} \mathrm{~d} x=\ln \frac{7}{2} \text {. }$ Find the value of the positive constant $$$a$$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m20_qp_22 Year：2020 Question No：3

Answer:

Integrate to obtain $k \ln (2 x-5)$
Apply limits to obtain $\ln (6 a-5)-\ln (2 a-5)=\ln \frac{7}{2}$
Apply subtraction law for logarithms
Obtain equation $\frac{6 a-5}{2 a-5}=\frac{7}{2}$
Solve equation for $a$
Obtain $a=\frac{25}{2}$

Knowledge points:

2.1.1 understand the meaning of |x| , sketch the graph of y = |ax + b| and use relations such as |a| = |b| a - b < x < a + b when solving equations and inequalities (Graphs of and for non-linear functions are not included.)

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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