Project #35006 - Problem 1

1. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 

x=6 y^2, y = 1, x = 0, about the y-axis 

2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 

y=x^2, x = y^2 about the axis x= -8

3. The region between the graphs of \(x=y^2\) and \(x=6 y\) is rotated around the line \(y=6\). 

The volume of the resulting solid is

4. A car drives down a road in such a way that its velocity ( in m/s) at time t (seconds) is \[v(t) = 1 t^{1/2} + 4\]. 

Find the car's average velocity (in m/s) between \(t = 4\) and \(t = 6\). 

5.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 = 6 x^2 and y = x^2 + 9. 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

6. Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 

y=e^{1 x}, y=e^{4 x}, x=

7. 

Subject Mathematics
Due By (Pacific Time) 07/08/2014 11:00 pm
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