All Flashcards
Define Accumulation Function.
A function defined by a definite integral where one of the limits of integration is a variable.
What does the Fundamental Theorem of Calculus relate?
Differentiation and integration; it shows they are inverse processes.
What is the integrand?
The function inside the integral that is being integrated.
What is a definite integral?
An integral with upper and lower limits, resulting in a numerical value.
What is an antiderivative?
A function whose derivative is the original function.
What is the upper bound of an integral?
The upper limit of integration in a definite integral.
What is the lower bound of an integral?
The lower limit of integration in a definite integral.
Define the Chain Rule.
A rule for differentiating composite functions.
What is the derivative?
The instantaneous rate of change of a function with respect to its variable.
What is integration?
The process of finding the area under a curve.
How to find if ?
Apply the Fundamental Theorem of Calculus: .
How to find if ?
Apply the Fundamental Theorem of Calculus and the Chain Rule: .
How to find given ?
First find using the Fundamental Theorem of Calculus, then evaluate .
How to find if ?
First, switch the limits: . Then, .
How to find if ?
Split the integral: . Then, .
How do you evaluate ?
Apply the Fundamental Theorem of Calculus and the chain rule: .
How do you find if ?
Apply the Fundamental Theorem of Calculus: .
How do you solve for if ?
First find . Then, .
How do you find the derivative of ?
Switch the bounds and apply the Fundamental Theorem of Calculus: , so the derivative is .
How do you find if ?
Switch the bounds: . Apply the Fundamental Theorem of Calculus and the chain rule: .
What is the formula for the Fundamental Theorem of Calculus (Part 1)?
What is the formula for switching the bounds of integration?
What is the formula for the Fundamental Theorem of Calculus (Part 1) with a function in the upper limit?
What is the general form of an accumulation function?