Question #3a4e1

1 Answer
Demirari
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.

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