What is the area of the region between 2 consecutive polnts where the graphs of f(x)=cos(x) and g(x)=-cos(x)+2 intersect? Choose 1 answer: (A) 4 (B) 4pi (C) 2 (D) 2pi

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Find Intersection Points: First, we need to find the points of intersection between the two functions f(x) = cos(x) and g(x) = -cos(x) + 2.Set Equations Equal: To find the points of intersection, we set f(x) equal to g(x): cos(x) = -cos(x) + 2Solve for x: Solving for x, we add cos(x) to both sides of the equation: cos(x) + cos(x) = 2 2cos(x) = 2Identify x Values: Divide both sides by 2 to isolate cos(x): cos(x) = 1Calculate Areas: The value of x for which cos(x) = 1 is x = 2nπ, where n is an integer. However, we are looking for the first two consecutive points of intersection, so we will consider n = 0 and n = 1.Determine Total Area: The first point of intersection is at x = 0, and the second point of intersection is at x = 2π. These are the consecutive points where the two graphs intersect.Now, we need to find the area of the region between these two points. The graphs of f(x) and g(x) are symmetrical about the line y = 1, and the area between them from x = 0 to x = 2π is a pair of identical ＂bumps＂ above and below y = 1.The area of one ＂bump＂ above y = 1 is the same as the area of one ＂bump＂ below y = 1. Since the total area from x = 0 to x = 2π under the curve y = cos(x) is 2π (the integral of cos(x) from 0 to 2π), the area of one ＂bump＂ is half of that, which is π.Therefore, the total area of the region between the two graphs from x = 0 to x = 2π is twice the area of one ＂bump,＂ which is 2 * π = 2π.

What is the area of the region between $2$ consecutive polnts where the graphs of $f(x)=\cos (x)$ and $g(x)=-\cos (x)+2$ intersect? $\newline$ Choose $1$ answer: $\newline$ (A) $4$ $\newline$ (B) $4 \pi$ $\newline$ (C) $2$ $\newline$ (D) $2 \pi$

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What is the area of the region between 222 consecutive polnts where the graphs of f(x)=cos⁡(x) f(x)=\cos (x) f(x)=cos(x) and g(x)=−cos⁡(x)+2 g(x)=-\cos (x)+2 g(x)=−cos(x)+2 intersect?\newlineChoose 111 answer:\newline(A) 444\newline(B) 4π 4 \pi 4π\newline(C) 222\newline(D) 2π 2 \pi 2π

What is the area of the region between $2$ consecutive polnts where the graphs of $f(x)=\cos (x)$ and $g(x)=-\cos (x)+2$ intersect? $\newline$ Choose $1$ answer: $\newline$ (A) $4$ $\newline$ (B) $4 \pi$ $\newline$ (C) $2$ $\newline$ (D) $2 \pi$