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Math 1710 Exam 3

Show all work (i.e., work things out on paper, not in your head).



4. Use the tangent line to a graph, or differentials, to approximate the value of

(69)[1/3] , knowing that (64)[1/3] = 4 . (15 pts.)


1. Find the following definite and indefinite integrals (9 pts. each):

(a) (x2+1)(x-2)  dx

(b) x(1-2x2)[2/3]  dx

(c) 02 x3-5x+3  dx

(d) sec4 xtanx  dx

(e) 13 [x/([(x2+1)])]  dx

2. (15 pts.) Find the area of the region lying between the graphs of

f(x) = x2-3x+8 and g(x) = 3x

3. (20 pts.) Find the volume of the solid region obtained by revolving the region in the plane bounded by graphs of

y = [(4-x2)], y = x, and x = 0

around the x-axis (see figure).



Figure

4. (20 pts.) Find the volume of the solid region obtained by revolving the region in the plane bounded by graphs of

y = x[(8-x3)] and y = 0

around the y-axis (see figure).



Figure


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