Question #3a4e1

1 Answer
Jan 17, 2018

area = 2pi m^2

Explanation:

First, let us integrate the two functions. Since they are both similar with the only difference in being constants, we can integrate one and assume the other integral.

First, we know that intsin(x)dx = -cos(x) + C and that int1dx = x + C. Combining these two, we would get -cos(x) + x.

Then we can assume that the integral of sin(x)+2 is -cos(x)+2x.

While we can calculate the values of these two functions with their upper and lower-bounds , we can recognize that we can subtract the two functions together to get x.

We subtract as we wish to find the area between the upper and lower sine waves.

Then finding the upper limit, we get 2pi and the lower limit to be 0, there forth the area is 2pi.

Note: The upper limit is 2pi as that is the maximum length of the walkway and the lower limit is 0 as we assume the walkway starts at the origin.