Which of the following statements is true?The double integral of the function f(x,y) =over the region in the first quadrantyA32xbounded by the lines y=x, y=2x, x=1, and x=3 is given by ||dydx.1The area of the region bounded by the line y= - x and the parabola x =y-yВ2is given by the double integral |у-dxdy.'yThe volume of the solid that is bounded above by the paraboloid z = x² + y? and below by thetriangle enclosed by the lines y=2x, x=0, and x + y= 6 in the xy- plane is given by6-x(x² + y?)dydx.

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Answered: The double integral of the function…

The double integral of the function f(x,y) = over the region in the first quadrant y A 3, 2x bounded by the lines y=x, y=2x, x=1, and x=3 is given by dydx. y

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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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 selection of the best element for a given system.

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, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

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 that have length, breadth, and height (or depth).

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.

Question

Which of the following statements is true?
The double integral of the function f(x,y) =
over the region in the first quadrant
y
A
3
2x
bounded by the lines y=x, y=2x, x=1, and x=3 is given by ||
dydx.
1
The area of the region bounded by the line y= - x and the parabola x =y-y
В
2
is given by the double integral |
у-
dxdy.
'y
The volume of the solid that is bounded above by the paraboloid z = x² + y? and below by the
triangle enclosed by the lines y=2x, x=0, and x + y= 6 in the xy- plane is given by
6-x
(x² + y?)dydx.

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