I need the answers for these 4 HW problems. Thank you! 1. Find the volume of the
ID: 3348202 • Letter: I
Question
I need the answers for these 4 HW problems. Thank you!
1.Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
3. Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep safe. Since Dr. Jones is a mathematician, she suggests building fences described by y=7x2 and y=x2+5. Farmer Jones thinks this would be much harder than just building an enclosure with straight sides, but he wants to please his wife. What is the area of the enclosed region?
4. The region between the graphs of x=y2 and x=5y is rotated around the line y=5.
The volume of the resulting solid is?
Explanation / Answer
Since we have y in terms of x and a horizontal axis, let's use washers. Each washer has outer radius R = y = 9 - x ² and inner radius r = 0, so V = ?[a,b] ?(R ² - r ²) dx = ??[-3,3] (81 - 18x ² + x^4) dx V = (?)(81x - 6x ³ + x^5/5) |[-3,3] = (?)(243-162+243/5) V = (1296?)/5= 1296?/5 ? 813.8