How do we set up integrals for Ex. 1. Let S be a solid bounded by two parallel planes perpendicular to the y- axis at y= c andy=d. If, for each y in c, d, the cross-sectional area of S perpendicular to the y-axis isdA(y), then the volume of the solid is V = A(y) dy provided A(y) is integrable.Ex. 1Derive the formula for the volume of a right pyramid whose altitude is h and whosebase is a square with sides of length a.A-axisB(0, h)sT-axisa.0)(a)B,h-yJ'(b)

Answered: Derive the formula for the volume of a…

Derive the formula for the volume of a right pyramid whose altitude is h and whose base is a square with sides of length a.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

How do we set up integrals for Ex. 1.

Let S be a solid bounded by two parallel planes perpendicular to the y- axis at y= c and
y=d. If, for each y in c, d, the cross-sectional area of S perpendicular to the y-axis is
d
A(y), then the volume of the solid is V = A(y) dy provided A(y) is integrable.
Ex. 1
Derive the formula for the volume of a right pyramid whose altitude is h and whose
base is a square with sides of length a.
A-axis
B(0, h)s
T-axis
a.0)
(a)
B,
h-y
J'
(b)

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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