Representation of Specific Antiderivatives

 

The Two Fundamental Theorems of Calculus

Course Material Related to This Topic:

Statement and explanation of the First and Second Fundamental Theorems, with examples.

Using the Fundamental Theorem to evaluate an integral.

Eight questions which involve functions defined with integrals, and these functions must be described, evaluated, or used to prove some statement.

Course Material Related to This Topic:

Fundamental Theorem of Calculus is presented and justified.

Using the Fundamental Theorem to evaluate the derivative of a function which is defined in terms of an integral.

Course Material Related to This Topic:

Statement and explanation of the two forms for the Fundamental Theorem of Calculus.

Upward arrow. Back to Top

The Second Fundamental Theorem: Continuous Functions Have Antiderivatives

Explanation of the implications and applications of the Second Fundamental Theorem, including an example.

Course Material Related to This Topic:

Upward arrow. Back to Top

Defining New Functions

Using the Second Fundamental Theorem to define the natural logarithm function and the error function, including diagrams and examples.

Course Material Related to This Topic:

Upward arrow. Back to Top

Proof of the Two Fundamental Theorems

An intuitive argument justifying the Second Fundamental Theorem and a complete proof of the First Fundamental Theorem, inluding remarks about these theorems as they relate to definite and indefinite integrals.

Course Material Related to This Topic:

Upward arrow. Back to Top

Functions Defined By Integrals

Course Material Related to This Topic:

Three part question finding bounds on the values of a function defined in terms of an integral and finding where the function is concave up or concave down.

Four part question which involves finding the derivative, critical points, and an estimation of a function which is defined in terms of an integral.

Four part question which involves finding critical points and values of a function which is defined in terms of an integral.

Finding the first and second derivatives of a function defined in terms of an integral, and expressing another integral in terms of that function.

Upward arrow. Back to Top