MAT180-HY1 Calculus 1

#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=8x2y=8x2 and y=x2+12y=x2+12. 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 Points possible: 1. Total attempts: 2

Sketch the region enclosed by y=6xy=6x and y=4x2y=4x2. Find the area of the region.    

#3 Points possible: 1. Total attempts: 2

Sketch the region enclosed by y=e5xy=e5x, y=e8xy=e8x, and x=1x=1. Find the area of the region.    

#4 Points possible: 1. Total attempts: 2

Find the area between the curves y=e−0.8xy=e-0.8x and y=1.5x+1y=1.5x+1 from x=0x=0 to x=5x=5. Area =    

#5 Points possible: 1. Total attempts: 2

Sketch the region enclosed by y=2xy=2x and y=2x2y=2x2. Decide whether to integrate with respect to xx or yy. Then find the area of the region.    

#6 Points possible: 1. Total attempts: 2

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to xx or yy. Then find the area of the region. y=6x2y=6x2, y=x2+7y=x2+7