1.Find f.

f ”(t) = 3et + 6 sin t,f(0) = 0,f(Ï€) = 0

2.Find f.

f ”(x) = x−2,x > 0,f(1) = 0,f(6) = 0

3.Find a function f such that
f ‘(x) = 3×3
and the line
3x + y = 0
is tangent to the graph off.

4.Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the y-axis.

y = 7e−x2,y = 0,x = 0,x = 1

5.Use the method of cylindrical shells to find the volumeV generated by rotating the region bounded by the given curves about they-axis.

 
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