Wednesday, January 4
−
Lecture 2 :
Integration by parts
(Refers to 6.2 in your text )
Students who have practiced the techniques presented in this lecture should be able to
:
Recognize those
integrals which are best integrated by the technique "
Integration by parts
", apply the technique of
integration by
parts
to integrate appropriate integrals, compute definite integrals by the “
integration by parts
” method.
2.1
Antiderivatives of less common functions
−
At this point it is a good idea to review
the derivatives of less common elementary functions. In particular recalling the following
derivatives will help to find the integral of some functions in the future. For example if
we know that the derivative of
a
x
is
a
x
ln(
a
) we don’t have to prove that the indefinite
integral of
a
x
ln
a
is
a
x
+
C
.
Question

Let's see if we understand this correctly.
We see that
So arcsin
x + C =
arccos
x + C.
Does this mean that arcsin
x
=
arccos
x
? Explain!
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 Winter '08
 ZHOU
 Calculus, Derivative, Integrals, Integration By Parts, Compute definite integrals

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