Finding area between two cosine curves

Question

I must to find the area between these two curves:

$$y = 2 \cos 7x, y = 2 − 2 \cos 7x$$ $$0 ≤ x ≤ π/7$$

And this is all I have so far:

$$ 2\cos7x=2-2\cos7x $$ $$4\cos7x=2$$ $$\cos7x=1/2$$

Answer 1

So, you know the two curves intersect at $7p = \cos^{-1} (1/2)$, which implies $p = (\pm \pi/3 + 2\pi k)/7$ for any $k \in \mathbb{Z}$.

For which $k$ do we observe an intersection within the specified integral of integration? That is, for which $k$ is $p \in [0, \pi/7]$? (Hint: there is only one such $k$)

The last step is to integrate $f(x) - g(x)$ from $0$ to $p$ and then integrate $g(x) - f(x)$ from $p$ to $\pi/7$, where $f$ is the larger of $y_1 = 2\cos7x$ and $y_2 = 2 - 2\cos7x$ on the interval $[0, p)$, and $g$ is the larger on the interval $(p, \pi/7]$.