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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 7, Problem 95RE
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Calculus: An Applied Approach (Min...

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Ron Larson
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Volume of a Solid Region In Exercises 93-96, use a double integral to find the volume of the solid region.

Chapter 7, Problem 95RE, Finding the Volume of a Solid Region In Exercises 93-96, use a double integral to find the volume of

To determine

To calculate: The volume of the solid region shown below by application of double integral

Calculus: An Applied Approach (MindTap Course List), Chapter 7, Problem 95RE

Explanation

Given Information:

The provided solid region is shown below as;

Formula used:

To determine the volume of a solid follow the steps provided below as:

Step 1: First write the equation of the surface in form,

z=f(x,y)

Which is followed by sketching of solid region

Step 2: Next sketch the region R in the two-dimensional x-y plane and then find the order and limits of integration.

Step 3: Finally solve the obtained double integral,

∫R∫f(x,y)dA

By using the necessary information from step 2.

The integration of function f(x)=xn,n≠−1 is;

∫xndx=xn+1n+1+c

Calculation:

Consider the provided solid region.

The equation of the surface is z=4 which is already in the z=f(x,y) form.

Next sketch the graph of region R in the x-y plane shown below as,

By observation of the above graph it is clear that the region R is bounded by the equations y=0,x=2 and y=x

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Sect-7.1 P-1CPSect-7.1 P-2CPSect-7.1 P-3CPSect-7.1 P-4CPSect-7.1 P-5CPSect-7.1 P-6CPSect-7.1 P-7CPSect-7.1 P-1SWUSect-7.1 P-2SWUSect-7.1 P-3SWU
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a Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the ...

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In Exercises 23-32, determine whether the statement is true or false. Give a reason for your choice. 28. (22 3...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

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Statistics for The Behavioral Sciences (MindTap Course List)

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Single Variable Calculus

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Probability and Statistics for Engineering and the Sciences

In Exercises 53 to 62, use set notation to describe the shaded region. You may use any of the following symbols...

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Mathematical Applications for the Management, Life, and Social Sciences

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Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums ...

Single Variable Calculus: Early Transcendentals

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Contemporary Mathematics for Business & Consumers

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Elementary Geometry For College Students, 7e

Prove that 23 is not a rational number.

Elements Of Modern Algebra

Identify the period for each of the following. Do not sketch the graph. y=tan(3x)

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Rate of Change A point moves along the curve y=x in such a way that the y-component of the position of the poin...

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Finite Mathematics for the Managerial, Life, and Social Sciences

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Finding and Evaluating Partial DerivativesIn Exercises 2730, find all first partial derivatives, and evaluate e...

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Police records show the following numbers of daily crime reports for a sample of days during the winter months ...

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Graph each ellipse. (x1)225+y24=1

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A shaft is being cut in a lathe. The tool feeds (advances) 0.015 inch each time the shaft turns once (1 revolut...

Mathematics For Machine Technology

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Introduction To Statistics And Data Analysis

Describe in your own words the criteria that the IRB uses to evaluate proposed research.

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In a single-case research study consisting of a series of phases, how long should each phase be and what factor...

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Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the followingvalues of n and x. a. n = 4...

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