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  1. AP Calculus
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Applications of Integration

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

Given the solid whose base is the region in the xy-plane bounded by y=x2y=x^2y=x2 and y=2xy=2xy=2x, if cross-sections perpendicular to the x-axis are semicircles, which integral represents the volume of this solid?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

The graphs of y=x2−4y = x^2 - 4y=x2−4 and y=2x−x2y = 2x - x^2y=2x−x2 create a bounded area that is the base of a solid. This solid has cross sections that are perpendicular to the xxx-axis and form squares. Which equation gives the length of one side of a single square cross section for some xxx value?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

When finding the volume of a solid with semicircular cross-sections perpendicular to the y-axis over interval [a, b], if r(y) represents radius at height y, how should you set up your integral?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

What would be an integral expression for calculating the volume of a solid whose base lies on region bounded by y=xy=xy=x and y=x3y=x^3y=x3, if every cross-section perpendicular to y-axis is an equilateral triangle?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

For a solid with circular cross-sections perpendicular to the y-axis, which variable represents the radius if these circles are drawn from (0,y)(0,y)(0,y) to (f(y),y)(f(y),y)(f(y),y)?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

The base of a solid with square cross sections is bounded by x−1\sqrt{x-1}x−1​, x=3x = 3x=3, y=0y = 0y=0. What is the volume of this solid?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

Given that semicircles are constructed perpendicularly to the x-axis over [a, b], what represents the correct formula for calculating their combined volume if their radii at any point x satisfy r(x)=sin(x)r(x) = \\sin(x)r(x)=sin(x)?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

For a region in the first quadrant bounded by y=xy=xy=x and y=e−xy=e^{-x}y=e−x rotated about y-axis, if one were to set up an integral using cylindrical shells method for finding volume, what would be its correct form?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

The graphs of y=x2−4y = x^2 - 4y=x2−4 and y=2x−x2y = 2x - x^2y=2x−x2 create a bounded area that is the base of a solid. This solid has cross sections that are perpendicular to the xxx-axis and form squares. What formula for A(x)A(x)A(x) should be used in the Volume integral for this solid?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

Which formula can be used to find the volume of a solid with square cross sections over an interval [a,b]?