Show all work for credit. Do all your work neatly on the paper provided. Write your name on each sheet you turn in. I will not grade any work done on the test sheet. When you are finished turn in all sheets including the test. Good Luck.

1. Approximate the area of the region bounded by y = 4x, the x-axis, the line x = 0, and the line x = 2. Divide the interval [0,2] into 4 subintervals of equal length and use a convenient point in each subinterval, to determine the areas of the chosen collection of rectangles.

2. Evaluate the following sums:

   (a) å_{j = 1}³ j³              (b) å_{j = 3}⁵ [j/( j+1)]

3. Evaluate the following integrals:

   1. ò([(-3)/( x^{[3/ 11]})] + [2/( x^3/₉)])dx

   2. ò₂³ (s-1)(s-2)ds

   3. ò₄⁹ [(x+1)/( Öx)]dx

   4. ò_-2¹ |x|dx

   5. ò(sec²x-secxtanx)dx

4. Let F(x) = ò₁^x2 [1/( t²)] dt. Find F¢(x).

5. Carry out the indicated integration (Use substitution when necessary)

   1. òx²(11+2x³)^1/₃dx

   2. ò[2x/( [Ö(1+x²)])]  dx

   3. òsin²x cosx  dx

6. Find the area bounded by y = (x-1)²+2, the x-axis, the line x = -1, and the line x = 3.

(BONUS 5pts) Let L(x) be a function which has the property that L¢(x) = ¹/_x.
Find ò[sinx/ cosx] dx in terms of L.

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