Review topics for Exam II
Integration by substitution (5.3)
Differential equations (5.4)
Area under the graph of a positive function. Riemann sums.
Definition of a Riemann integrable function on [a,b].
Theorem: a continuous function on a closed interval is Riemann
Simple examples of functions not continuous, yet integrable.
The definite integral of f(x) on [a,b] (the Riemann integral) is the area between the graph of f and the
segment [a,b] with sign.
Calculation of areas as limits of Riemann sums.
And the other way around: calculation of limits of sums noting that
they are Riemann sums.
The Fundamental Theorem of Calculus.
Properties of definite integrals.
Area between two curves.
Volumes of solids of revolution: disk (or washer) method, cylindrical
Volumes by integrating the areas of the cross-sections.
Area of a surface of revolution.
e^x and ln: they are inverse to each other, limits for e, their
domains, range, derivatives, graphs,
integrating 1/x, and e^x (as such or in combination with