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AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 8

Lesson 7: Volumes with cross sections: squares and rectangles

Volumes with cross sections: squares and rectangles

AP.CALC: CHA‑5 (EU), CHA‑5.B (LO), CHA‑5.B.1 (EK)

Let R be the region enclosed by the curves y, equals, square root of, x, end square root and y, equals, start fraction, x, divided by, 3, end fraction.

Region R is the base of a solid whose cross sections perpendicular to the x-axis are squares.

Which one of the definite integrals gives the volume of the solid?

(Choice A)
integral, start subscript, 0, end subscript, start superscript, 1, end superscript, left parenthesis, square root of, x, end square root, minus, start fraction, x, divided by, 3, end fraction, right parenthesis, squared, d, x
(Choice B)
integral, start subscript, 0, end subscript, cubed, left parenthesis, square root of, x, end square root, minus, start fraction, x, divided by, 3, end fraction, right parenthesis, squared, d, x
(Choice C)
integral, start subscript, 0, end subscript, start superscript, 9, end superscript, left parenthesis, square root of, x, end square root, minus, start fraction, x, divided by, 3, end fraction, right parenthesis, squared, d, x
(Choice D)
integral, start subscript, 0, end subscript, start superscript, 27, end superscript, left parenthesis, square root of, x, end square root, minus, start fraction, x, divided by, 3, end fraction, right parenthesis, squared, d, x

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AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 8

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