Fundamental theorem of cal Flashcards
What is fundamental theorem of calculus in words and formulas?
Connects sides of calculus. Differential and integral.
Pic
Do all continuous functions have antiderivatives?
yes
Do all continuous functions have derivatives?
No, e.g. |x| has cusp at zero
T/F: The integral of function f(x) can be computed using any one of its infinitely many antiderivaitve
true.
Useful b/c finding the integration can use symbolic instead of numeric calculation
What are conditions for the first fundamental theorem
Note: f(x) is smooth (continuous) AND a is in domain of f(x)
derivative of the integral is the equation
get the variable to the top of integral: Use negative sign to flip top and bottom
Undestanding the fundamental theorems together
pic
base must be 2
Whats an indefinite integral?
The family of functions of antiderivatives
Id indefinite integral a number?
No, its a function.
Definite is a number
STUDY THIS
chain rule
LHOSPITAL RULE
KNOW THIS ONE
if see something with its derivative, think u substitution.
absolut value bc cannot be zero
negative goes to exponent
1/cos = sec
remember to rewrite the bounds
