AP®MathsCollege BoardCalculus ABExam QuestionsUnit 8: Applications of IntegrationAreas

Areas (College Board AP® Calculus AB)

Exam Questions

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1
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What is the area of the region in the first quadrant bounded by the graph of y equals e to the power of x over 3 end exponent and the line x equals 3?

  • 3 e minus 3

  • 3 e

  • e over 3 minus 1

  • fraction numerator e minus 1 over denominator 3 end fraction

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2
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If 0 less or equal than k less than pi and the area under the curve y equals sin x from x equals 0 to x equals k is 1.2, then k equals

  • 0.201

  • 1.772

  • 2.940

  • 4.511

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3
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The function f is defined by f open parentheses x close parentheses equals open curly brackets table row cell 5 minus x space space space for space x less or equal than 2 end cell row cell 3 space space space space space space space space space for space x greater than 2 end cell end table close. What is the value of integral subscript negative 1 end subscript superscript 6 f open parentheses x close parentheses space d x?

  • 21

  • 23.5

  • 25.5

  • 27

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4
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Let R be the region bounded by the graph of x equals ln y, the vertical line x equals 1, and the horizontal lines y equals e and y equals 5. Which of the following gives the area of R?

  • integral subscript 1 superscript ln 5 end superscript e to the power of x space italic d x

  • integral subscript e superscript 5 ln y space italic d y

  • integral subscript 1 superscript ln 5 end superscript open parentheses e to the power of x minus 5 close parentheses space italic d x

  • integral subscript e superscript 5 open parentheses ln y minus 1 close parentheses space italic d y

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5
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What is the area of the region between the graphs of y equals square root of x and y equals negative x from x equals 0 to x equals 4?

  • 8 over 3

  • 32 over 3

  • 40 over 3

  • 24

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