1. The number of gallons of gas consumed by the average american in one
year.
2. e - 1.
3. x - ln |x+2| + C
4. (x^3+1)^(7/3)/7 - (x^3+1)^(4/3)/4 + C
5. 3x^2 ln(x^3) - ln(e^x) = 9x^2 ln x - x.
6. Discs method: integral from 1 to 10 of pi*((2 + ln x)^2 - 4)dx
Shell method: integral from 0 to ln(10) of 2pi*(2+y)*(10-e^y) dy
7. 1/50 radians/sec.
8. (-1/3, 4*sqrt(2)/3) and (-1/3, -4*sqrt(2)/3).