The exam will cover the material we have studied in chapters seven and sixteen of the textbook, techniques of integration and sequences and series. In more detail:

Techniques of Integration:

Substitution: You were assumed to know this already, but clearly you cannot carry out the other techniques if you cannot do this. In particular you should be able to deal with a definite integral, either changing the limits of integration to match the changed variable or else completing the integral and substituting back the original variable before using the limits.
Powers of trigonometric functions, using trig identities. Some identities will be supplied in a table with the exam problems: At the course home page you can find a copy of that table.
Sums and differences of squares, using a trigonometric substitution. You need to be able to get back to the original variable, if an indefinite integral, and to use the limits of integration, if a definite integral: These can be a lot easier to carry out if you draw a picture to motivate the substitution rather than just using a remembered trick.
Completing the square: This frequently gives rise to a problem requiring a trig substitution, and it is easy to make algebraic errors in carrying this out.
Integration by parts: You should be able to handle situations where the resulting integral again requires work such as another application of parts, or where the final result is achieved by solving algebraically.
Improper integrals: Integrals where a limit is explicitly infinite are "easy" in the sense that they call attention to being improper and requiring a limiting process. Be sure to check whether any integral is improper because the integrand causes problems somewhere inside the interval: If you do such an integral without taking a limit, even if you get the correct answer, you will probably receive no credit.

 

Sequences and Series:

Be sure to think about the difference between a sequence and a series, and not to operate on one as if it were the other!
Convergence of sequences: What does it mean for a sequence to converge, and what does it converge to? (I won't ask you to give a formal proof that a sequence converges, but you should be able to give good informal reasons for stating that a sequence converges or diverges, and you should be able to find what most convergent sequences converge to.)
Infinite series: The definition of the infinite sum in terms of a limit of a sequence, and terminology such as the n-th partial sum. You might be asked to find a formula for the n-th partial sum of a series, but only for a telescoping or geometric series. You should be able to multiply a series by a constant, and to add or subtract two series.
Special series: You should recognize and be able to work with geometric series, the harmonic series, and p-series.
Convergence tests:
For geometric series
The n-th term test
For non-negative series: Comparison, Integral, ratio, and n-th root tests. You will not have to use an integral to estimate a remainder.
For series which may have some negative terms: Absolute vs. conditional convergence
For alternating series: Leibniz' theorem. You should be able to do remainder estimation for alternating series.
Power series:
The radius and interval of convergence
Term-by-term integration and differentiation within the interval of convergence
Producing or recognizing Maclaurin or Taylor series or polynomials
Taylor's theorem with remainder: You may use either the integral form of the remainder term, given with the first statement of Taylor's theorem in the text, or Lagrange's form. You should be able to use the remainder term to show whether the series converges to f(x) and to estimate remainders. You should be able to do remainder estimation in either direction: What is the error if we use n terms, or how many terms do we need to get the error within a certain bound.