1. Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field

Question

1. 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=6x2 and y=x2+3. 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?

2. Sketch the region enclosed by y=3x and y=9x2. Find the area of the region.

3. Sketch the region enclosed by y=e2x, y=e7x, and x=1. Find the area of the region.

4. Find the volume of the solid obtained by rotating the region bounded by y=7x2, x=2, x=4 and y=0, about the x-axis.

Explanation / Answer

1)y=6x2 and y=x2+3

6x2 =x2+3

5x2 =3

x2 =3/5

x=-(3/5),x=(3/5)

area=[-(3/5) to (3/5)] x2+3 -6x2dx

area=[-(3/5) to (3/5)] 3 -5x2dx

area=[-(3/5) to (3/5)] 3x -(5/3)x3 +c

area=[3(3/5) -(5/3)((3/5))3 +c]-[3(-(3/5)) -(5/3)(-(3/5))3 +c]

area=[3(3/5) -(3/5) +c]-[-3(3/5) +(3/5) +c]

area=[2(3/5)]-[-2(3/5) ]

area=4(3/5)

area =3.1

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