Integration by Parts
Every differentiation rule has a corresponding integration
rule. For instance, the Substitution Rule for integration
corresponds to the Chain Rule for differentiation. The rule
that corresponds to the Product Rule for differentiat
7.2 Trigonometric Integrals
In this section we use trigonometric identities to integrate
certain combinations of trigonometric functions.
We start with powers of sine and cosine.
Find sin5x cos2x dx.
We could convert cos2x to 1 sin2x
7.5 Strategy for Integration
In this section we present a collection of miscellaneous
integrals in random order and the main challenge is to
recognize which technique or formula to use.
No hard and fast rules can be given as to which method
applies in a g
7.3 Trigonometric Substitution
In finding the area of a circle or an ellipse, an integral of the
dx arises, where a > 0.
If it were
the substitution u = a2 x2 would be
effective but, as it stands,
dx is more difficult.
If we change the variable fro
7.4 Integration of Rational Functions by Partial Fractions
In this section we show how to integrate any rational
function (a ratio of polynomials) by expressing it as a sum of
simpler fractions, called partial fractions, that we already
know how to integr
7.8 Improper Integrals
In this section we extend the concept of a definite integral to
the case where the interval is infinite and also to the case
where f has an infinite discontinuity in [a, b].
In either case the integral is called an improper integral
Department of Applied Mathematics
Calculus 1301B - Winter 2017, Section 06
Dr. Zinovi Krougly, Office MC 250
Phone 519 661 -2111 ext. 88787
Email [email protected]