is the
"Antiderivative" of 
when
. Calculus
Lesson
20 Antiderivatives
Back to Dr. Nandor's Calculus Notes Page
Back to Dr. Nandor's Calculus Page
Back to Dr. Nandor's Math Pages
is the
"Antiderivative" of when
.
Find 
:
What about adding a constant? If 
and 
, note that
they have the same derivative.
So if 
, then 
, where we
call 
the
"constant of integration."
So, here is the proper way to solve for a function, given its derivative:
Always think: what would I have to differentiate to get
this function?
Two ways to think about it:
More exmples: 
Sometimes you may have to re-write the polynomial or trig function:
Finally, note that 
,
thus far, could be anything. (Plot 
which
is the antiderivative of 
since
).
Pick an initial condition to solve . For instance, let's
say that we knew that 
.
REALLY FINALLY, solve the differential equation:
Back to Dr. Nandor's Calculus Notes Page
Back to Dr. Nandor's Calculus Page