AP®MathsCollege BoardCalculus ABExam QuestionsUnit 6: Integration & Accumulation of ChangeIntegration & Antiderivatives

Integration & Antiderivatives (College Board AP® Calculus AB)

Exam Questions

13 mins10 questions

Select a question set to download for
Integration & Antiderivatives

Select an answer set to view for
Integration & Antiderivatives

1
Sme Calculator1 mark

Work out the indefinite integral integral fraction numerator x squared plus x minus 12 over denominator x squared minus 3 x end fraction space d x.

How did you do?

Did this page help you?

2
Sme Calculator1 mark

Work out the indefinite integral integral open parentheses x to the power of 4 minus x plus 1 over x close parentheses squared space d x.

How did you do?

Did this page help you?

3
Sme Calculator2 marks

The rate of change of a curve is given by fraction numerator d y over denominator d x end fraction equals 3 x squared minus sin x. Given that the curve passes through the point open parentheses pi comma space 1 close parentheses, find the equation of the curve in terms of x.

How did you do?

Did this page help you?

4
Sme Calculator2 marks

The function A is used to model the surface area of a pond, in square meters, that is covered by a particular species of invasive pond weed. The rate of change function for A is A to the power of apostrophe, with the rate of change at time t given by A to the power of apostrophe open parentheses t close parentheses equals e to the power of negative t over 2 end exponent. Given that 1 square meter of the pond is covered by the weed at at time t equals 0 , find an expression for A open parentheses t close parentheses.

How did you do?

Did this page help you?

5
Sme Calculator2 marks

A function f satisfies the equation f to the power of apostrophe open parentheses x close parentheses equals fraction numerator x squared plus x plus 1 over denominator x cubed plus x end fraction, where f to the power of apostrophe is the derivative of f. Given that f open parentheses 1 close parentheses equals 0, find an expression for f open parentheses x close parentheses in terms of x.

How did you do?

Did this page help you?