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

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Chapter 8, Problem 126RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Electricity The oscillating current in an electrical circuit can be modeled by

I = 2   sin   60 π t + cos   120 π t where I is measured in amperes and t is measured in seconds. Find the average current for the time intervals (a) 0 ≤ t ≤ 1 240 ,

(b) 0 ≤ t ≤ 1 60 , and (c) 0 ≤ t ≤ 1 30 .

(a)

To determine

To calculate: The average current for interval 0≤t≤1240, when oscillating current in the circuit is given by expression I=2sin60πt+cos120πt.

Explanation

Given Information:

The oscillating current in the circuit is given by expression I=2sin60πt+cos120πt.

Formula used:

Write the formula for average value of a provided function f(x) for [a,b].

Average value=1b−a∫abf(x)dx

Write the formula for definite integral of ∫abcosnudu.

∫abcosnudu=[sinnun]ab

Here, n is the any number.

Write the formula for definite integral of ∫absinnudu.

∫absinudu=[−cosnun]ab

Calculation:

Consider the oscillating current in the circuit.

I=2sin60πt+cos120πt

Use the formula for average value to find average current for interval 0≤t≤1240, which can be mathematically written as:

average=11240−0∫01240Idt=240∫01240(2sin60πt+cos120πt)dt=240{2∫01240sin60πtdt+∫01240cos120πtd}

Use the above integral formulae to find integral of above expression

(b)

To determine

To calculate: The average current for interval 0≤t≤160, when oscillating current in the circuit is given by expression I=2sin60πt+cos120πt.

(c)

To determine

To calculate: The average current for interval 0≤t≤130, when oscillating current in the circuit is given by expression I=2sin60πt+cos120πt.

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 P-3SWUSect-8.2 P-4SWUSect-8.2 P-5SWUSect-8.2 P-6SWUSect-8.2 P-7SWUSect-8.2 P-8SWUSect-8.2 P-9SWUSect-8.2 P-10SWUSect-8.2 P-11SWUSect-8.2 P-12SWUSect-8.2 P-1ESect-8.2 P-2ESect-8.2 P-3ESect-8.2 P-4ESect-8.2 P-5ESect-8.2 P-6ESect-8.2 P-7ESect-8.2 P-8ESect-8.2 P-9ESect-8.2 P-10ESect-8.2 P-11ESect-8.2 P-12ESect-8.2 P-13ESect-8.2 P-14ESect-8.2 P-15ESect-8.2 P-16ESect-8.2 P-17ESect-8.2 P-18ESect-8.2 P-19ESect-8.2 P-20ESect-8.2 P-21ESect-8.2 P-22ESect-8.2 P-23ESect-8.2 P-24ESect-8.2 P-25ESect-8.2 P-26ESect-8.2 P-27ESect-8.2 P-28ESect-8.2 P-29ESect-8.2 P-30ESect-8.2 P-31ESect-8.2 P-32ESect-8.2 P-33ESect-8.2 P-34ESect-8.2 P-35ESect-8.2 P-36ESect-8.2 P-37ESect-8.2 P-38ESect-8.2 P-39ESect-8.2 P-40ESect-8.2 P-41ESect-8.2 P-42ESect-8.2 P-43ESect-8.2 P-44ESect-8.2 P-45ESect-8.2 P-46ESect-8.2 P-47ESect-8.2 P-48ESect-8.2 P-49ESect-8.2 P-50ESect-8.2 P-51ESect-8.2 P-52ESect-8.2 P-53ESect-8.2 P-54ESect-8.2 P-55ESect-8.2 P-56ESect-8.2 P-57ESect-8.2 P-58ESect-8.2 P-59ESect-8.2 P-60ESect-8.2 P-61ESect-8.2 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P-3QYSect-8.3 P-4QYSect-8.3 P-5QYSect-8.3 P-6QYSect-8.3 P-7QYSect-8.3 P-8QYSect-8.3 P-9QYSect-8.3 P-10QYSect-8.3 P-11QYSect-8.3 P-12QYSect-8.3 P-13QYSect-8.3 P-14QYSect-8.3 P-15QYSect-8.3 P-16QYSect-8.3 P-17QYSect-8.3 P-18QYSect-8.3 P-19QYSect-8.3 P-20QYSect-8.3 P-21QYSect-8.3 P-22QYSect-8.3 P-23QYSect-8.3 P-24QYSect-8.3 P-25QYSect-8.4 P-1CPSect-8.4 P-2CPSect-8.4 P-3CPSect-8.4 P-4CPSect-8.4 P-5CPSect-8.4 P-6CPSect-8.4 P-7CPSect-8.4 P-8CPSect-8.4 P-9CPSect-8.4 P-1SWUSect-8.4 P-2SWUSect-8.4 P-3SWUSect-8.4 P-4SWUSect-8.4 P-5SWUSect-8.4 P-6SWUSect-8.4 P-7SWUSect-8.4 P-8SWUSect-8.4 P-9SWUSect-8.4 P-10SWUSect-8.4 P-1ESect-8.4 P-2ESect-8.4 P-3ESect-8.4 P-4ESect-8.4 P-5ESect-8.4 P-6ESect-8.4 P-7ESect-8.4 P-8ESect-8.4 P-9ESect-8.4 P-10ESect-8.4 P-11ESect-8.4 P-12ESect-8.4 P-13ESect-8.4 P-14ESect-8.4 P-15ESect-8.4 P-16ESect-8.4 P-17ESect-8.4 P-18ESect-8.4 P-19ESect-8.4 P-20ESect-8.4 P-21ESect-8.4 P-22ESect-8.4 P-23ESect-8.4 P-24ESect-8.4 P-25ESect-8.4 P-26ESect-8.4 P-27ESect-8.4 P-28ESect-8.4 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P-7SWUSect-8.5 P-8SWUSect-8.5 P-9SWUSect-8.5 P-10SWUSect-8.5 P-11SWUSect-8.5 P-12SWUSect-8.5 P-13SWUSect-8.5 P-14SWUSect-8.5 P-15SWUSect-8.5 P-16SWUSect-8.5 P-17SWUSect-8.5 P-18SWUSect-8.5 P-19SWUSect-8.5 P-20SWUSect-8.5 P-1ESect-8.5 P-2ESect-8.5 P-3ESect-8.5 P-4ESect-8.5 P-5ESect-8.5 P-6ESect-8.5 P-7ESect-8.5 P-8ESect-8.5 P-9ESect-8.5 P-10ESect-8.5 P-11ESect-8.5 P-12ESect-8.5 P-13ESect-8.5 P-14ESect-8.5 P-15ESect-8.5 P-16ESect-8.5 P-17ESect-8.5 P-18ESect-8.5 P-19ESect-8.5 P-20ESect-8.5 P-21ESect-8.5 P-22ESect-8.5 P-23ESect-8.5 P-24ESect-8.5 P-25ESect-8.5 P-26ESect-8.5 P-27ESect-8.5 P-28ESect-8.5 P-29ESect-8.5 P-30ESect-8.5 P-31ESect-8.5 P-32ESect-8.5 P-33ESect-8.5 P-34ESect-8.5 P-35ESect-8.5 P-36ESect-8.5 P-37ESect-8.5 P-38ESect-8.5 P-39ESect-8.5 P-40ESect-8.5 P-41ESect-8.5 P-42ESect-8.5 P-43ESect-8.5 P-44ESect-8.5 P-45ESect-8.5 P-46ESect-8.5 P-47ESect-8.5 P-48ESect-8.5 P-49ESect-8.5 P-50ESect-8.5 P-51ESect-8.5 P-52ESect-8.5 P-53ESect-8.5 P-54ESect-8.5 P-55ESect-8.5 P-56ESect-8.5 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Finite Mathematics

Find the indicated roots. Sketch the roots in the complex plane. 38. The fifth roots of 32

Single Variable Calculus: Early Transcendentals

Evaluate each expression: 3+17(22)67

Elementary Technical Mathematics

Prove each of the following identities. csc2sin=cos2sin

Trigonometry (MindTap Course List)

Answer true or false for review Exercises 1 to 7. The value of a ratio must be less than 1.

Elementary Geometry For College Students, 7e

Let f(x)=a0+a1x++an1xn1+xn be a monic polynomial of positive degree n with coefficients that are all integers. ...

Elements Of Modern Algebra

EXHIBIT 20-5 Corporate Bond Quotation Table-the Wall Street Journal Online (1) (2) (3) (4) (5) (6) (7) (8) (9) ...

Contemporary Mathematics for Business & Consumers

Using a Right Triangle In Exercises 19-24, use the figure to write the expression in algebraic form given y=arc...

Calculus of a Single Variable

WRITING ABOUT CONCEPTS Moments of Inertia Give the formulas for findingthe moments of inertia about the x-and y...

Calculus: Early Transcendental Functions (MindTap Course List)

Use d=x2-x12+y2-y12 to find the length of CD- as described in Exercise 2. _ In the coordinate system for Exerci...

Elementary Geometry for College Students

Suppose payments will be made for 914 years at the end of each month into an ordinary annuity earning interest ...

Finite Mathematics for the Managerial, Life, and Social Sciences

True or False: If f′(x) = g′(x), then f(x) = g(x).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

Using Vectors to Determine Collinear Points In Exerciser 67-70, use vectors to determine whether the points are...

Multivariable Calculus

From the Maclaurin series for ln(1 + x) and sin x, the first three terms of the Maclaurin series for (ln(1 + x)...

Study Guide for Stewart's Multivariable Calculus, 8th

The data from exercise 2 follow. xi 3 12 6 20 14 yi 55 40 55 10 15 a. Compute the mean square error using equat...

Statistics for Business & Economics, Revised (MindTap Course List)

What is the goal of a hypothesis test?

Research Methods for the Behavioral Sciences (MindTap Course List)

Identify and describe the content of each section of an APA-style research report.

Research Methods for the Behavioral Sciences (MindTap Course List)

Suppose that you were asked to help design a survey of adult city residents in order to estimate the proportion...

Introduction To Statistics And Data Analysis

Solve each problem. Mowing lawns Julie can mow a lawn with a lawn tractor in 2 hours, and her husband can mow t...

College Algebra (MindTap Course List)

The median price of homes in Austin, Texas is 248,640 (AustinHomeSearch website, April 2015). A sample of 200 h...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In each of the following exercises, the value on the left must be multiplied by one of the following numbers: 0...

Mathematics For Machine Technology

Using Properties of the GradientIn Exercises 2938, find the gradient of the function and the maximum value of t...

Calculus (MindTap Course List)

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