is
the antiderivative of 
writtenWetzel
Math 140
4.1 – Antiderivatives and Indefinite Integration
Antiderivative – given a derivative, finding the original function.
is
the antiderivative of written
=
if and only if 
Indefinite Integral = Antiderivative
Example
Integration Rules –
Constant Rule -
=
where k is a constant
Ex.:
1.) 
2.) 
Power Rule -
=
where 
Ex.:
3.) 
4.) 
Coefficient Rule -
=
Ex.:
5.) 
6.) 
Sum / Difference Rule -
Ex.:
7.) 
8.) 
Trig. Integrals –
Ex.:
9.) 
10.) 
Particular Solutions -
Ex.:
11 Find the general solution of
and
find the particular solution at the point (1, 4).
HW: p. 255 #15-41odd