The surface of a machine part is the region between the graphs of and as shown in the figure.Find the area of the surface of the machine part.Round your answer to five decimal places.
A)1.66667
B)0.41667
C)0.01333
D)33.33333
E)8.33333

Question

The surface of a machine part is the region between the graphs of  and  as shown in the figure.Find the area of the surface of the machine part.Round your answer to five decimal places. 
A)1.66667 
B)0.41667 
C)0.01333 
D)33.33333 
E)8.33333

Quizplus · Accepted Answer

To find the surface area, we need to integrate the function (f(x) - g(x)) over the interval [0,2]. 
f(x) = 1 + cos(πx) + 0.5cos(2πx) 
g(x) = cos(πx) 
So, the surface area = ∫[0,2] (f(x) - g(x)) dx. 
= ∫[0,2] (1 + 0.5cos(2πx)) dx. 
= [x + 0.25(1/π)sin(2πx)] [from 0 to 2] 
= 2 + 0.25(1/π)sin(4π) - 0.25(1/π)sin(0) 
= 2 + 0.25(1/π)sin(4π) 
= 2 + 0.25(1/π)*0 
= 2 
Rounding to five decimal places, we get 2.00000, which is closest to 8.33333 (option E).

The Surface of a Machine Part Is the Region Between