Chapter 4 - Antiderivative Flashcards
What is an Antiderivative?
A function F is called antiderivative of f on an interval I IF F’(X) = f(x) for all x in I
What is the Antiderivative Theorem?
If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is..
F(x) + C
What is the antiderivative of cf(x)?
cF(x)
what is the antiderivative of f(x) + g(x)?
F(x) + G(x)
what is the antiderivative of X^n (n cannot equal 1)?
X^(n+1)/n +1
What is the antiderivative of (1/x)?
ln|x|
What is the antiderivative of e^x?
e^x/(derivative of x) + C
what is the antiderivative of cos(x)?
sin(x)
What is the antiderivative of sin(x)?
-cos(x)
What is the antiderivative of sec^2(x)?
tan(x)
What is the antiderivative of sec(x)tan(x) ?
sec(x)
What is the antiderivative of 1/√ (1 - x^2)?
arcsin(x)
What is the antiderivative of 1/√ (1 + ^2) ?
arctan(x)
What is the antiderivative of cosh(x) ?
sinh(x)
what is the antiderivative of sinh(x) ?
cosh(x)