It can be shown that the area enclosed between the x-axis and one arch of the sine curve is 2. Use this fact to compute the
definite integral.
-$$\int _ { \pi } ^ { 2 \pi } 2 | \cos x | d x$$
A) 0
B) 2
C) 4
D) 8

Question

Quizplus · Accepted Answer

The integral $\int _ { \pi } ^ { 2 \pi } 2 | \cos x | d x$ can be interpreted as twice the area under the curve of $|\cos x|$ from $\pi$ to $2\pi$. Since $|\cos x|$ is the absolute value of the cosine function, it reflects the negative parts of the cosine curve above the x-axis, making the area under $|\cos x|$ from $\pi$ to $2\pi$ identical to the area under the sine curve from 0 to $\pi$, which is given as 2. Therefore, the integral evaluates to $2 \times 2 = 4$.

It Can Be Shown That the Area Enclosed Between the X-Axis