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1998 MC Non Calculator Integral Probs

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by

Richard Matto

on 9 March 2013

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Transcript of 1998 MC Non Calculator Integral Probs

12 Integral Problems From
1998 AP Calc Test (AB)
Multiple Choice
Non Calculator Portion
The other 16 elsewhere. 25 Look For
The other 16 MC Problems from 1998
Calculator Portion Of Multiple Choice 17 Problems
6 Open Ended Problems (2 with Calculator, 4 Without) Integrals (without absolute value) can
be thought of as the "Area above the x-axis"
- "Area below the x-axis"... This is displacement

If you are looking for "Total Distance", take the integral
of absolute value. This will be.."Area above the x-axis"
+ "Area below the x-axis"
Need to keep straight.
Derivative of the integral
Evaluating integral
Don't integrate
Plug in top, times CR of top
- Plug in bottom, times CR of Bottom Find antiderivative
Plug in top - plug in bottom Integrating tools (for AB)
Algebra First
U-Substitution Distribute
Simplify
Break up fractions
Rewrite with exponents For definite integrals
choose U, insert constants as needed
CHANGE the bounds
Take anti-derivative of U expression
Plug in top U - Plug in Bottom U
***Don't go back to x values Know the 2 types of derivative of an integral
Most open ended problems
Easy...Constant for lower bound, x for upper bound
Some Multiple Choice Problems
More work....Variable expressions (with CR) in
top, bottom or both bounds Don't Integrate
Simply replace "t" with "x" Plug in top times CR of top
- plug in bottom times CR of bottom
(**CR of a constant = 0) ADVICE "AVERAGE"

From algebra, "Average Rate of Change"
.... Slope of secant line [f(b) - f(a)]/(b - a)
.... This is like finding the average velocity
if you are given a position function.

Average of a Function = integral/interval
....given f(x), find average of f(x)
....given position function, find average position
Must integrate and then divide by the interval
Full transcript