Which of the following expressions gives the volume when region R is rotated about the line ?
A)
B)
C)

Question

​Which of the following expressions gives the volume when region R is rotated about the line  ? ​
A)​ 
B)​ 
C)​

Quizplus · Accepted Answer

The expression for the volume when a region is rotated about a line is given by π ∫a^b f(x)^2 dx, where f(x) is the distance from the line of rotation to the function. In this case, the line of rotation is x = 5 and the distance from the line to the function is 5 - x. Therefore, the integral to find the volume is π ∫0^5 (5 - x)^2 dx, which simplifies to π ∫0^5 (x^2 - 10x + 25) dx. Evaluating the integral gives π [95/3] = 31.4159... which corresponds to choice C.

​Which of the Following Expressions Gives the Volume When Region

Which of the Following Expressions Gives the Volume When Region