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Statement and explanation of the First and Second Fundamental Theorems, with examples.
Explanation of the implications and applications of the Second Fundamental Theorem, including an example.
Using the Second Fundamental Theorem to define the natural logarithm function and the error function, including diagrams and examples.
Fundamental Theorem of Calculus is presented and justified.
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.
Statement and explanation of the two forms for the Fundamental Theorem of Calculus.
Using the Fundamental Theorem to evaluate the derivative of a function which is defined in terms of an integral.
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.
Using the Fundamental Theorem to evaluate an integral.
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.
Eight questions which involve functions defined with integrals, and these functions must be described, evaluated, or used to prove some statement.