Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

6th Edition

ISBN: 9781418300203

Author: Prentice Hall

Publisher: Prentice Hall

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Question

Chapter 5, Problem 10RE

To determine

To find the total volume using Riemann sum approximation.

Expert Solution

Answer to Problem 10RE

Total volume =limn→∞∑i=1nπsin2m1(Δx) .

Explanation of Solution

Given:

The radius is given by r=sinmi .

Formula used:

Surface of sphere were generated by revolving the graph of the function f(x)=sinx about the x-axis. The partition the interval into n subinterval of equal length Δx . Then since the sphere with planes perpendicular to the x-axis at the partition points, cutting it like a round loaf of bread into n parallel sides of width Δx . When n is large, each slice can be approximately by the cylinder of volume πr2h . h is Δx while r varies according to where are on the x-axis. A logical radius to choose for each cylinder is f(m1)=sin(m1) , where m1 is the midpoint of the interval where the ith , slice interest the x-axis.

Calculation:

Given radius is r=sinmi .

The volume of the sphere by using MRAM to sum the cylinder volumes,

Volume of one cylinder

V=πr2h V=π (sin( m i )) 2 ΔxV=πsin2(mi)Δx

Using Riemann sum approximation,

Total volume =limn→∞∑i=1nπsin2m1(Δx) .

To determine

To find function using numerical integration capability.

Expert Solution

Answer to Problem 10RE

The function is ∫abf(x)dx=NINT(f(x),x,a,b)

Explanation of Solution

Given:

The radius is given by r=sinmi .

Formula used:

The right-hand side of the equation is an approximation of the left-hand side.

Calculation:

Calculator has a numerical integration capability, which will denote as NINT. In particular, will use NINT(f(x),x,a,b) to denote a calculator approximation of ∫abf(x)dx .

∫abf(x)dx=NINT(f(x),x,a,b) .

The understanding that the right-hand side of the equation is an approximation of the left-hand side.

To determine

To find the value of function using the NINT.

The value of the function is 4.9348 .

Expert Solution

Answer to Problem 10RE

The value of the function is 4.9348 .

Explanation of Solution

Given:

The given function f(x)=πsin2x .

Formula used:

Calculator has a numerical integration capability, which will denote as NINT. In particular, will use NINT(f(x),x,a,b) to denote a calculator approximation of ∫abf(x)dx .

∫abf(x)dx=NINT(f(x),x,a,b) .

Calculation:

The given is f(x)=πsin2x .

∫abπsin2xdx=NINT(πsin2x,x,a,b)∫abπsin2xdx=4.9348.

Chapter 5, Problem 9RE

Chapter 5, Problem 11RE

Chapter 5 Solutions

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.2 - Prob. 1QR Ch. 5.2 - Prob. 2QR Ch. 5.2 - Prob. 3QR Ch. 5.2 - Prob. 4QR Ch. 5.2 - Prob. 5QR Ch. 5.2 - Prob. 6QR Ch. 5.2 - Prob. 7QR Ch. 5.2 - Prob. 8QR Ch. 5.2 - 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Prob. 62EP

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