/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 9 Consider the functionA(x)=鈭�0xt... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 9 (page 398)

Consider the function

A(x)=鈭�0xt2dt;B(x)=鈭�3xt2dt;

(a)TheobjectiveistoexplainwhytheirderivativesdifferbyaconstantbycomparingthederivativesofA(x)&B(x).(b)TheobjectiveistoexplainwhytheirderivativesdifferbyaconstantbycomparingthederivativesofA(x)-B(x).

Short Answer

Expert verified

(a)Thederivativesdifferbyconstant(b)Itissignedareaunderthegraphofy=x(2fromx=0tox=3.

Step by step solution

01

Step 1. Given 

The given function isA(x)=鈭�0xt2dt;B(x)=鈭�3xt2dt;

02

Part(a) Step 2. Explanation

ThederivativeofA(x)isA'(x)=x2..ThederivativeofB(x)B'(x)=x2.Therefore,thederivativesofA(x)&B(x)differbyaconstant.

03

Part(b) Step 3. Explanation

A(x)=鈭�0xt2dt;B(x)=鈭�3xt2dt;Whichmeansthatitisthesignedareaunderthegraphofy=x2fromx=0tox=3.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Approximations and limits: Describe in your own words how the slope of a tangent line can be approximated by the slope of a nearby secant line. Then describe how the derivative of a function at a point is defined as a limit of slopes of secant lines. What is the approximation/limit situation described in this section?

As n approaches infinity this sequence of partial sums could either converge meaning that the terms eventually approach some finite limit or it could diverge to infinity meaning that the terms eventually grow without bound. which do you think is the case here and why?

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating .

鈭�23x+1dx

Shade in the regions between the two functions shown here on the intervals (a) [鈭�2, 3]; (b) [鈭�1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?

Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = 12on [-蟺2,2蟺] ?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.