Find the exact value of $$\(\int_{\frac{1}{4} \pi}^{\frac{1}{2} \pi} 3 \sin x \cot \frac{1}{2} x d x\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_22 Year：2020 Question No：8(c)
Answer:
Express integrand in form \(a+b \cos x\)
Obtain correct integrand \(3+3 \cos x\)
Integrate to obtain \(p x+q \sin x\)
Apply limits correctly
Obtain \(\frac{3}{4} \pi+3-\frac{3}{\sqrt{2}}\) or exact equivalent
Obtain correct integrand \(3+3 \cos x\)
Integrate to obtain \(p x+q \sin x\)
Apply limits correctly
Obtain \(\frac{3}{4} \pi+3-\frac{3}{\sqrt{2}}\) or exact equivalent
Knowledge points:
2.5.2 use trigonometrical relationships in carrying out integration
Solution:
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