MA 126, Calculus 2 UAB, Fall 2004
TEST 1
Duration 70min;
Make sure to show all your work and underline the final results of each problem. Write your
name on this sheet and use it as a cover page when you turn in your work. Do not write
your results on this paper. Good luck!
1. The graph of fconsists of two straight lines and a semi circle. Use it to evaluate each
integral.
(a)Z4
3
f(x)dx, (b)Z2
0
f(x)dx, (c)Z4
1
f(x)dx
2. (a) Use the properties of integrals to verify that
Z3
1
1
ln(x)+2dx ≤1
(b) Derive a good lower bound for integral in a similar way as the upper bound is derived.
(E.g. −1 is a correct lower bound but not good enough.)
3. Write out the form of the partial fraction expansion of the function. Do not determine
the numerical values of the coefficients.
(a)4x−1
(x+ 1)2(x−3) (b)1+5x−x2
(x2+ 2x+ 6)(x−1)
4. Evaluate the following integrals
(a)Z2
1
s3ds
1
