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

Methods of Integration (College Board AP® Calculus AB)

Exam Questions

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Methods of Integration

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Methods of Integration

1
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Using the substitution u equals square root of x, integral subscript 4 superscript 9 fraction numerator cos square root of x over denominator square root of x end fraction space d x is equal to which of the following?

  • 1 half integral subscript 2 superscript 3 cos u space d u

  • 2 integral subscript 2 superscript 3 cos u space d u

  • integral subscript 4 superscript 9 cos u space d u

  • 2 integral subscript 4 superscript 9 cos u space d u

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2
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integral subscript 1 superscript 3 fraction numerator x squared over denominator x cubed plus 1 end fraction space d x equals

  • 1 third ln 3

  • 1 third ln 14

  • ln 3

  • ln 14

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3
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integral fraction numerator x over denominator square root of 1 minus 25 x squared end root end fraction space d x equals

  • 1 fifth arcsin open parentheses 5 x close parentheses plus C

  • x over 5 arcsin open parentheses 5 x close parentheses plus C

  • negative 1 over 25 square root of 1 minus 25 x squared end root plus C

  • negative 1 over 25 ln square root of 1 minus 25 x squared end root plus C

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4
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Let f be a function such that integral subscript 3 superscript 12 f open parentheses 3 x close parentheses space d x equals 9. Which of the following must be true?

  • integral subscript 1 superscript 4 f open parentheses t close parentheses space d t equals 3

  • integral subscript 3 superscript 12 f open parentheses t close parentheses space d t equals 27

  • integral subscript 3 superscript 12 f open parentheses t close parentheses space d t equals 3

  • integral subscript 9 superscript 36 f open parentheses t close parentheses space d t equals 3

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5
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integral open parentheses square root of 1 minus cos x end root space integral subscript 0 superscript x cos t space d t close parentheses space d x equals

  • cos x square root of 1 minus cos x end root plus C

  • open parentheses cos x minus 1 close parentheses square root of 1 minus cos x end root plus C

  • 3 over 2 open parentheses 1 minus cos x close parentheses plus C

  • table row blank blank cell 2 over 3 open parentheses 1 minus cos x close parentheses to the power of 3 over 2 end exponent plus C end cell end table

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