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

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# 1998 MC Non Calculator Integral Probs

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