Hence show that $$$\int_{\frac{1}{4} \pi}^{\frac{1}{3} \pi}(\operatorname{cosec} 2 \theta-\cot 2 \theta) \mathrm{d} \theta=\frac{1}{2} \ln 2$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_32 Year：2021 Question No：6(b)

Answer:

State integral of the form $\mp \ln \cos \theta$ or $\pm \ln \sec \theta$
Use correct limits correctly and insert exact values for the trigonometric ratios
Obtain a correct expression, e.g. $-\ln \frac{1}{2}+\ln \frac{1}{\sqrt{2}}$
Obtain $\frac{1}{2} \ln 2$ from correct working

Knowledge points:

3.2.1 understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)

Answer:

Knowledge points:

Solution:

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