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A force of 20 N is required to hold a spring that has been stretched from its natural length of 5 cm to a length of 15 cm. How much work is done in stretching the spring from 15 cm to 30 cm?

2. Evaluate by hand the indefinite integral

5. Use the shell method to find the volume generated by rotating the region bounded by the curves y = x3, y = 8, x = 0 about the y-axis. Draw a typical shell and label the dimensions that will be part of your integral. 

4. Use the disk method to find the volume of the solid obtained by rotating the region bounded by the curve y = 3x, the y-axis, and the line y = 6 about the y-axis.

A piece of steel that covers a region bounded by the x-axis, the curve y = x3 – 3x + 4, and the vertical lines x = 0 and x = 2 is deformed into a rectangle that stretches from x = 0 to x = 2. Use the concept of the average value of a function to find the height of the resulting rectangle.

6. Use the shell method to find the volume generated by rotating the region bounded by the curves y = x2, y = 0, x = 0 and x = 4 about the x-axis. Draw a typical shell and label the dimensions that will be part of your integral. 

Morgan wants to verify the official federal eligibility requirements for the education tax credit. Which source would be the most appropriate place to verify those requirements?

Morgan wants to determine whether an education tax credit can be claimed based on Morgan’s college attendance. Which additional information is most important to obtain before reaching a conclusion?

The South Florida Building Code, adopted in 2957, was seriously out of date; the effects of wind on the built environment are not thoroughly understood; and, the critical wind-engineering expertise of engineer and architects is largely absent when it comes to the design of residential construction. These lessons, according to the book resulted from: 

What rivers bounded the delta where the Sumerians lived almost 6000 years ago?