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10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 4, Problem 88RE

Textbook Problem

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Using the Trapezoidal Rule and Simpson's Rule In Exercises 87–90, approximate the definite integral using the Trapezoidal Rule and Simpson’s Rule with *n* = 4. Compare these results with the approximation of the integral using a graphing utility.

To determine

**To calculate:** The approximate value of the definite integral

**Given:**

The definite integral

**Formula used:**

Trapezoidal Rule: If *f* is a continuous function on

Where, *n* is the number of partitions, *a* is lower limit and *b* is upper limit of the integral.

Simpson’s Rule: If *f* is a continuous function on

**Calculation:**

For the given integral

Now,

For

For

For

For

For

Calculus

Show all chapter solutions

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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? The graph shows the flow rate...Ch. 4.5 - Sales The sales S (in thousands of units) of a...Ch. 4.5 - Electricity The oscillating current in an...Ch. 4.5 - Probability In Exercises 91 and 92, the function...Ch. 4.5 - Probability In Exercises 91 and 92, the function...Ch. 4.5 - Graphical Analysis Consider the functions f and g,...Ch. 4.5 - Finding a Limit Using a Definite Integral Find...Ch. 4.5 - Rewriting Integrals...Ch. 4.5 - Rewriting integrals (a). Show that...Ch. 4.5 - True or False? In Exercises 9196, determine...Ch. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - Rewriting Integrals Assume that f is continuous...Ch. 4.5 - Integration and Differentiation (a) Verify that...Ch. 4.5 - Proof Prove the second property of Theorem 4.16.Ch. 4.5 - Rewriting Integrals Show that if f is continuous...Ch. 4.5 - PUTNAM EXAM CHALLENGE If a0,a1,,an are real...Ch. 4.5 - PUTNAM EXAM CHALLENGE Find all the continuous...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 4.6 - WRITING ABOUT CONCEPTS Polynomial Approximations...Ch. 4.6 - Describing an Error Describe the size of the error...Ch. 4.6 - Estimating Errors In Exercises 2326, use the error...Ch. 4.6 - Estimating Errors In Exercises 2326, use the error...Ch. 4.6 - Estimating Errors In Exercises 2326, use the error...Ch. 4.6 - Estimating Errors In Exercises 2326, use the error...Ch. 4.6 - Estimating Errors In Exercises 2730, use the error...Ch. 4.6 - Estimating Errors In Exercises 2730, use the error...Ch. 4.6 - Estimating Errors In Exercises 2730, use the error...Ch. 4.6 - Estimating Errors In Exercises 2730, use the error...Ch. 4.6 - Estimating Errors Using Technology In Exercises...Ch. 4.6 - Estimating Errors Using Technology In Exercises...Ch. 4.6 - Estimating Errors Using Technology In Exercises...Ch. 4.6 - Estimating Errors Using Technology In Exercises...Ch. 4.6 - Finding the Area of a Region Approximate the area...Ch. 4.6 - Finding the Area of a Region Approximate the area...Ch. 4.6 - Area Use Simpsons Rule with n = 14 to approximate...Ch. 4.6 - Circumference The elliptic integral 830/2123sin2d...Ch. 4.6 - Surveying Use the Trapezoidal Rule to estimate the...Ch. 4.6 - HOW DO YOU SEE IT? The function f(x) isconcave...Ch. 4.6 - Work To determine the size of the motor required...Ch. 4.6 - Approximating a Function The table lists several...Ch. 4.6 - Approximation of Pi In Exercises 43 and 44, use...Ch. 4.6 - Approximation of Pi In Exercises 43 and 44, use...Ch. 4.6 - Using Simpson's Rule Use Simpsons Rule with n = 10...Ch. 4.6 - Proof Prove that Simpsons Rule is exact when...Ch. 4.6 - Proof Prove that you can find a polynomial p(x) =...Ch. 4 - Finding an Indefinite Integral In Exercises 18,...Ch. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Finding an Indefinite Integral In Exercises 18,...Ch. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Finding a Particular Solution In Exercises 9-12,...Ch. 4 - Finding a Particular Solution In Exercises 9-12,...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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