Explanation 1) Concept: Definition of volume: Let S be a solid that lies between x = a and x = b . If the cross sectional area of S in the plane P x , through x and perpendicular to the x - a x i s , is A ( x ) , where A is continuous function, then the volume of S is V = lim n → ∞ ⁡ ∑ i = 1 n A x i * ∆ x = ∫ a b A x d x 2) Given: b a s e = h e i g h t 3) Calculations: The red line segment ( s ) represents the base of cross section (isosceles triangle) at x . Area of an isosceles triangle is A = 1 2 · b a s e · h e i g h t Since, b a s e = h e i g h t , so area of cross section is A = 1 2 b a s e 2 Now the length of the base at x denoted s ( x ) is the distance from x-axis to the point ( x , 1 - x 2 ) . So s ( x ) = 1 - x 2 Now area of cross section at x is

8th Edition

ISBN: 9781337051545

Author: Stewart

Publisher: CENGAGE C

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 5.2, Problem 59E

To determine

To find:

The volume of the solid S whose base is the region enclosed by parabola y=1-x2

And cross sections perpendicular to the x-axis are isosceles triangles with height equal to the base.

Expert Solution & Answer

Chapter 5 Solutions

UD CALC (241 ONLY) W/1 TERM ACCESS >IB

Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Prob. 3E Ch. 5.1 - Find the area of the shaded region.Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Sketch the region enclosed by the given curves....Ch. 5.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The volume of the solid S whose base is the region enclosed by parabola y = 1 - x 2 And cross sections perpendicular to the x - a x i s are isosceles triangles with height equal to the base.

Solution Summary: The author calculates the volume of the solid S, whose base is the region enclosed by parabola and cross sections perpendicular to the x-axis, are isosceles triangles with height equal

Concept explainers

Videos

To find:

The volume of the solid S whose base is the region enclosed by parabola y=1-x2

And cross sections perpendicular to the x-axis are isosceles triangles with height equal to the base.

Chapter 5 Solutions

The volume of the solid S whose base is the region enclosed by parabola y = 1 - x 2 And cross sections perpendicular to the x - a x i s are isosceles triangles with height equal to the base.

Solution Summary: The author calculates the volume of the solid S, whose base is the region enclosed by parabola and cross sections perpendicular to the x-axis, are isosceles triangles with height equal

Concept explainers

Videos

To find: The volume of the solid S whose base is the region enclosed by parabola y=1-x2 And cross sections perpendicular to the x-axis are isosceles triangles with height equal to the base.

Chapter 5 Solutions

To find:

The volume of the solid S whose base is the region enclosed by parabola y=1-x2

And cross sections perpendicular to the x-axis are isosceles triangles with height equal to the base.