Calculus: Key Concepts (9/8/10)

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Presentation transcript:

Calculus: Key Concepts (9/8/10) What are the 3 or 4 key concepts of calculus?

The Definite Integral What does it mean to “integrate a function” over some part of its domain? That is, given a function f (x) defined on an interval [a, b], what does mean? How can we compute this number?

Antiderivatives Given a function f (x), what is an antiderivative of f ? Why do we say “an”, not “the”? Is computing antiderivatives mechanical process like computing derivatives? Do all elementary functions have formulas for their antiderivatives?

Recall Some Derivative Facts d/dx (x r) = (What can r be?) d/dx (a x) = d/dx (loga(x)) = d/dx (sin(x)) = d/dx (tan(x)) = d/dx (arcsin(x)) = d/dx (e x^2) =

Recall (?) Some Antiderivative Facts x r dx = (provided r  ?) 1/x dx = a x dx = loga(x) dx = sin(t) dt = tan(t) dt = arcsin(x) dx = e(x^2) dx =

Assignment for Friday Obtain or reunite yourself with the text and read page 387 on the Fundamental Theorem. Review the derivative and antiderivative facts we discussed in class and review all the rules for finding derivatives. Remember to always bring your text and your clicker (oh, and your brain!) to class.