Summary SINGLE VARIABLE CALCULUS AND DIFFERENTIAL EQUATION FOR NON MAJORS

SINGLE VARIABLE
CALCULUIS AND
DIFFERENTIAL
EQUATIONS FOR NON
MAJORS

, The Antiderivative
The reverse operation of finding a derivative is called the
antiderivative. A function F is an antiderivative of a function f if
dF ( x )
= f (x)
dx
1) Find the antiderivative of F ( x ) = 5 Theorem 1:
Find several functions that have the derivative of 5 If a function
has more than
Answer; 5x, 5x + 3, 5x −12 one
2) Find the antiderivative of F ( x ) = x 2 antiderivative,
then the
Find several functions that have the derivative of x2 antiderivatives
differ by at
1 3 ; or 1 x3 + ; or 1 x3 − e most a constant.
Answer: x
3 3 3

, Indefinite Integral
The expression:
 f (x)dx
read “the indefinite integral of f with respect to x,”
means to find the set of all antiderivatives of f.


 f (x)dx x is called the variable
of integration

Integral sign Integrand

, Constant of Integration
Every antiderivative F of f must be of
the form  f ( x ) dx = F( x ) + C where C is
a constant of integration.



Notice 6xdx = 3x2 + C


Represents every possible
antiderivative of 6x.