Applications of Integration
Given the solid whose base is the region in the xy-plane bounded by and , if cross-sections perpendicular to the x-axis are semicircles, which integral represents the volume of this solid?
The graphs of and create a bounded area that is the base of a solid. This solid has cross sections that are perpendicular to the -axis and form squares. Which equation gives the length of one side of a single square cross section for some value?
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?
What would be an integral expression for calculating the volume of a solid whose base lies on region bounded by and , if every cross-section perpendicular to y-axis is an equilateral triangle?
For a solid with circular cross-sections perpendicular to the y-axis, which variable represents the radius if these circles are drawn from to ?
Radius equals .
Radius equals .
Radius equals .
Radius equals .
The base of a solid with square cross sections is bounded by , , . What is the volume of this solid?
4
1
8
2
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 ?

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For a region in the first quadrant bounded by and 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?
The graphs of and create a bounded area that is the base of a solid. This solid has cross sections that are perpendicular to the -axis and form squares. What formula for should be used in the Volume integral for this solid?
w * h
1/2(b*h)
s^2
1/2(pi*r^2)
Which formula can be used to find the volume of a solid with square cross sections over an interval [a,b]?
V =
V =
V =
V =