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Calculus

10th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781285057095
Chapter 4.4, Problem 68E
Textbook Problem
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Evaluating a Definite Integral In Exercises 67–72, find F as a function of x and evaluate it at x = 2, x = 5, and x = 8.

F ( x ) = 2 x ( t 3 + 2 t 2 ) d t

To determine

To calculate: The function F(x) and evaluate it for x=2,x=5 and x=8 provided that F(x)=2x(t3+2t2)dt.

Explanation of Solution

Given:

The integral F(x)=2x(t3+2t2)dt.

Formula used:

The integral abtndt=tn+1n+1|ab.

Calculation:

Consider the provided integral and solve it

F(x)=2x(t3+2t2)dt=t44+2t222t|2x=(x44+x22x)(4+44)=x4+4x28x164

For x=2 the value of F(x) is

F(x)=

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Differential Equation In Exercises 2730, solve 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 3342,...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 Equation Exercises 49-52, find an...Ch. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - 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HOW DO YOU SEE IT? 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Finding a Particular Solution In Exercises 9-12,...Ch. 4 - Finding a Particular Solution In Exercises 7-12,...Ch. 4 - Slope Field In Exercises 13 and 14, a differential...Ch. 4 - Slope Field In Exercises 13 and 14, a differential...Ch. 4 - Velocity and Acceleration A ball is thrown...Ch. 4 - Velocity and Acceleration The speed of a car...Ch. 4 - Velocity and Acceleration An airplane taking off...Ch. 4 - Modeling Data The table shows the velocities (in...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 21 and 22, use...Ch. 4 - Using Sigma Notation In Exercises 17 and 18, use...Ch. 4 - Evaluating a Sum In Exercises 19-24, use the...Ch. 4 - Evaluating a Sum In Exercises 19-24, 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 1924, use the...Ch. 4 - 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Evaluating a Definite Integral In Exercises 7582,...Ch. 4 - Evaluating a Definite Integral In Exercises 7582,...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 - Using an Even Function Use 02x4dx=325 to evaluate...Ch. 4 - 86. Respiratory Cycle After exercising for a few...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4 - Using the Trapezoidal Rule and Simpson's Rule In...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 - 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 - 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 - Using a Continuous Function Let f be continuous on...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 - Sine Integral Function The sine integral function...Ch. 4 - Comparing Methods Let I=04f(x)dx where f is shown...Ch. 4 - Minimizing an Integral Determine the limits of...

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Find the limit or show that it does not exist. limx1+x6x4+1

Single Variable Calculus: Early Transcendentals, Volume I

Solve the equations in Exercises 126. (x3+1)x+1(x3+1)2x+1=0

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 33-38, rewrite the expression using positive exponents only. 37. 120(s + t)3

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

For the following set of stores, find the value of each expression: a. X b. (X) c. (X 3) d. (X 3) X 4 5 2 1 3

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Factor completely: 8m210m3

Elementary Technical Mathematics

Finding an Indefinite Integral In Exercises 5-28, find the indefinite integral. 4x3+3x4+3xdx

Calculus: Early Transcendental Functions (MindTap Course List)

The general solution to dydt=ky is: a) y(t) = y(0)ekt b) y(t) = y(k)et c) y(t) = y(t)ek d) y(t) = ey(0)kt

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