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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275347

Chapter 4.4, Problem 73E

Textbook Problem

Finding and Checking an Integral In Exercises 69-74, (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a).

Expert Solution

**(a)**

To determine

**To calculate:** The value of

**Given:**

The function,

**Formula used:**

The integration will be broken to parts according to

Also,

Expert Solution

**(b)**

To determine

**To calculate:** The value of obtained function

Calculus (MindTap Course List)

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In Exercises 109 and 110, determine...Ch. 4.4 - True or False? In Exercises 109 and 110, determine...Ch. 4.4 - Analyzing a Function Show that the function...Ch. 4.4 - Finding a Function Find the function f(x) and all...Ch. 4.4 - Finding Values Let G(x)0x[s0sf(t)dt]ds where f is...Ch. 4.4 - Proof Prove that...Ch. 4.4 - PUTNAM EXAM CHALLENGE For each continuous function...Ch. 4.5 - CONCEPT CHECK Constant Multiple Rule Explain how...Ch. 4.5 - CONCEPT CHECK Change of Variables In your own...Ch. 4.5 - CONCEPT CHECK The General Power Rule for...Ch. 4.5 - CONCEPT CHECK Analyzing the Integrand Without...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Slope Field In Exercises 35 and 36, a differential...Ch. 4.5 - Slope Field In Exercises 35 and 36, a differential...Ch. 4.5 - Differential Equation In Exercises 37 and 38, the...Ch. 4.5 - Differential Equation In Exercises 37 and 38, the...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding a Limit In Exercises 49-52, find the...Ch. 4.5 - Finding a Limit In Exercises 49-52, find the...Ch. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Finding the Area of a Region In Exercises 69-72,...Ch. 4.5 - Finding the Area of a Region In Exercises 69-72,...Ch. 4.5 - 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Even and Odd Functions In Exercises 79 and 80,...Ch. 4.5 - EXPLORING CONCEPTS Choosing an Integral You are...Ch. 4.5 - EXPLORING CONCEPTS Comparing Methods Find the...Ch. 4.5 - Depreciation The rate of depreciation dV/dt of a...Ch. 4.5 - HOW DO YOU SEE IT? 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Finding a Particular Solution In Exercises 7-12,...Ch. 4 - Vertical Motion A ball is thrown vertically upward...Ch. 4 - Vertical Motion With what initial velocity must an...Ch. 4 - Finding a Sum In Exercises 15 and 16, find the sum...Ch. 4 - Finding a Sum In Exercises 15 and 16, find the sum...Ch. 4 - Using Sigma Notation In Exercises 17 and 18, use...Ch. 4 - Using Sigma Notation In Exercises 17 and 18, use...Ch. 4 - Evaluating a Sum In Exercises 1924, use the...Ch. 4 - Evaluating a Sum In Exercises 1924, use the...Ch. 4 - Evaluating a Sum In Exercises 1924, use the...Ch. 4 - Evaluating a Sum In Exercises 1924, use the...Ch. 4 - Evaluating a Sum In Exercises 19-24, use the...Ch. 4 - Evaluating a Sum In Exercises 19-24, use the...Ch. 4 - Finding Upper and Lower Sums for a Region In...Ch. 4 - Finding Upper and Lower Sums for a Region In...Ch. 4 - Finding Area by the Limit Definition In Exercises...Ch. 4 - Finding Area by the Limit Definition In Exercises...Ch. 4 - Finding Area by the Limit Definition In Exercises...Ch. 4 - Finding Area by the Limit Definition In Exercises...Ch. 4 - Finding Upper and Lower Sums for a Region In...Ch. 4 - Finding Upper and Lower Sums for a Region In...Ch. 4 - Approximating Area with the Midpoint Rule In...Ch. 4 - Approximating Area with the Midpoint Rule In...Ch. 4 - Evaluating a Definite Integral as a Limit In...Ch. 4 - Evaluating a Definite Integral as a Limit In...Ch. 4 - Evaluating a Definite Integral Using a Geometric...Ch. 4 - Evaluating a Definite Integral Using a Geometric...Ch. 4 - Using Properties of Definite Integrals Given...Ch. 4 - Using Properties of Definition Integrals Given...Ch. 4 - Evaluating a Definite Integral In Exercises 41-46,...Ch. 4 - Evaluating a Definite Integral In Exercises 41-46,...Ch. 4 - Evaluating a Definite Integral In Exercises 41-46,...Ch. 4 - Evaluating a Definite Integral In Exercises 41-46,...Ch. 4 - Finding the Area of a Region In Exercises 49-52,...Ch. 4 - Finding the Area of a Region In Exercises 49-52,...Ch. 4 - Evaluating a Definite Integral In Exercises 41-46,...Ch. 4 - Evaluating a Definite Integral In Exercises 41-46,...Ch. 4 - Using the Mean Value Theorem for Integrals In...Ch. 4 - Using the Mean Value Theorem for Integrals In...Ch. 4 - Finding the Average Value of a Function In...Ch. 4 - Finding the Average Value of a Function In...Ch. 4 - Finding the Area of a Region In Exercises 47 and...Ch. 4 - Finding the Area of a Region In Exercises 47 and...Ch. 4 - Using the Second Fundamental Theorem of Calculus...Ch. 4 - Using the Second Fundamental Theorem of Calculus...Ch. 4 - Finding the Area of a Region In Exercises 49-52,...Ch. 4 - Finding the Area of a Region In Exercises 49-52,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Finding an Indefinite Integral In Exercises 59-66,...Ch. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Finding the Area of a Region In Exercises 73 and...Ch. 4 - Finding the Area of a Region In Exercises 73 and...Ch. 4 - Even and Odd Functions In Exercises 75 and 76,...Ch. 4 - Even and Odd Functions In Exercises 75 and 76,...Ch. 4 - Using a Function Let L(x)=1x1tdt,x0 (a) Find L...Ch. 4 - Parabolic Arch Archimedes showed that the area of...Ch. 4 - Using a Continuous Function Let f be continuous on...Ch. 4 - Fresnel Function The Fresnel function S is defined...Ch. 4 - Approximation TheTwo-Point Gaussian Quadrature...Ch. 4 - Extrema and Points of Inflection The graph of the...Ch. 4 - Falling Objects Galileo Galilei (15641642) stated...Ch. 4 - Use the techniques of this chapter to verify this...Ch. 4 - Use the techniques of this chapter to verify this...Ch. 4 - Riemann Sum Use an appropriate Riemann sum to...Ch. 4 - Riemann Sum Use an appropriate Riemann sum to...Ch. 4 - Proof Let f be integrable on [a, b] and 0mf(x)M...Ch. 4 - Velocity and Acceleration A car travels in a...Ch. 4 - Proof Prove that if f is a continuous function on...Ch. 4 - Verifying a Sum Verify that i=1ni2=n(n+1)(2n+1)6...Ch. 4 - Evaluating a Sum and a Limit In Exercises 3 and 4,...Ch. 4 - Evaluating a Sum and a Limit In Exercises 3 and 4,...Ch. 4 - Sine Integral Function The sine integral function...Ch. 4 - Upper and Lower Sums Consider the region bounded...Ch. 4 - Minimizing an Integral Determine the limits of...Ch. 4 - Finding a Function The graph of f' is shown. 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