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

Integration & Antiderivatives (College Board AP® Calculus AB)

Exam Questions

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Integration & Antiderivatives

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Integration & Antiderivatives

1
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The derivative of a function f is f to the power of apostrophe open parentheses x close parentheses equals fraction numerator 3 over denominator 2 square root of x end fraction minus 2 x.

Given that f open parentheses 4 close parentheses equals negative 8, find f open parentheses x close parentheses.

  • f open parentheses x close parentheses equals x to the power of 3 over 2 end exponent minus x squared

  • f open parentheses x close parentheses equals 3 square root of x minus x squared plus 2

  • f open parentheses x close parentheses equals 3 square root of x minus x squared

  • f open parentheses x close parentheses equals 3 square root of x minus x squared minus 8

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2
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integral csc x space cot x space d x equals

  • negative csc x plus C

  • negative cot x plus C

  • negative fraction numerator csc squared x over denominator 2 end fraction plus C

  • negative fraction numerator cot squared x over denominator 2 end fraction plus C

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3
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integral subscript 1 superscript e open parentheses fraction numerator 3 x squared minus 1 over denominator x end fraction close parentheses space d x equals

  • 3 e minus 1 over e

  • 3 e squared minus e

  • fraction numerator 3 e squared over denominator 2 end fraction minus 5 over 2

  • 3 e squared minus 1

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4
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If f is a linear function, then integral f to the power of apostrophe apostrophe end exponent open parentheses x close parentheses space d x equals

  • 0

  • C

  • f to the power of apostrophe open parentheses x close parentheses

  • f open parentheses x close parentheses

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5
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integral sec squared x space d x equals

  • 1 third sec cubed x plus C

  • csc squared x plus C

  • sin squared x plus C

  • tan x plus C

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