The region encoded by: x = y^2 and y = x-2 is revolved around the line x= -3. Solve all the parts below

Question

The region encoded by: x = y² and y = x-2 is revolved around the line x= -3. Solve all the parts below

A). Find the points of intersection algebraically

B). Draw the picture

C). Write an integral which will give the volume of the solid. (Do not evaluate)

If possible please explain the step by step process in a video.

Answer 1

A). x = (x - 2)²; x² - 5x + 4 = 0; x = 1 or x = 4; y = - 1 or y = 2. Points of intersection (1, - 1) and (4, 2)

B) You can get graph by TI84

C) v = π∫_-1²[(y + 5)² - (y² + 3)²]dy