Integral Calculus (id: 74aa549f2)

本题目来源于试卷: Integral Calculus，类别为 IB数学

[问答题]
Consider the functions f and g qxrs dsgfcgy*9* 347sw*rm3udeyju t9qy8q;vdj5;,y0bq bjz9 fined on the domain $0\lt x\lt 2 \pi$ by

$f(x)=4 \cos 2 x \text { and } g(x)=2-8 \cos x $.


The following diagram shows the graphs of y=f(x) and y=g(x) .

1. Find the x -coordinates of the points of intersection of the two graphs.
2. Find the exact area of the shaded region, giving your answer in the form $a \pi+b \sqrt{3}$ , where a, b $\in \mathbb{Q}$ .

At the points P and Q on the diagram, the gradients of the two graphs are equal.
3. Determine the y -coordinate of P on the graph of g .

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