Explanation Definitions used: Regular x region: “A region R in the xy plane is a regular x region if there exist functions f ( x ) and g ( x ) and numbers a and b such that R = { ( x , y ) | g ( x ) ≤ y ≤ f ( x ) , a ≤ x ≤ b } ”. Regular y region: “A region R in the xy plane is a regular y region if there exist functions h ( y ) and k ( y ) and numbers c and d such that R = { ( x , y ) | h ( y ) ≤ x ≤ k ( y ) , c ≤ y ≤ d } ”. Calculation: Compute the given integral with respect y . ∫ 0 2 [ ∫ x 3 4 x ( 1 + 2 y ) d y ] d x = ∫ 0 2 [ ∫ x 3 4 x d y + 2 ∫ x 3 4 x y d y ] d x = ∫ 0 2 [ [ y ] x 3 4 x + 2 [ y 2 2 ] x 3 4 x ] d x = ∫ 0 2 [ [ y ] x 3 4 x + [ y 2 ] x 3 4 x ] d x Apply the limits of y . ∫ 0 2 [ ∫ x 3 4 x ( 1 + 2 y ) d y ] d x = ∫ 0 2 [ 4 x − x 3 ] + [ ( 4 x ) 2 − ( x 3 ) 2 ] d x = ∫ 0 2 [ 4 x − x 3 + 16 x 2 − x 6 ] d x Compute the integral with respect x . ∫ 0 2 [ ∫ x 3 4 x ( 1 + 2 y ) d y ] d x = 4 ∫ 0 2 x d x − ∫ 0 2 x 3 d x + 16 ∫ 0 2 x 2 d x − ∫ 0 2 x 6 d x = 4 [ x 2 2 ] 0 2 − [ x 4 4 ] 0 2 + 16 [ x 3 3 ] 0 2 − [ x 7 7 ] 0 2 = [ 2 x 2 ] 0 2 − [ x 4 4 ] 0 2 + 16 [ x 3 3 ] 0 2 − [ x 7 7 ] 0 2 Apply the limits of x . ∫ 0 2 [ ∫ x 3 4 x ( 1 + 2 y ) d y ] d x = [ 2 ( 2 ) 2 − 0 ] − [ 2 4 4 − 0 ] + 16 [ 2 3 3 − 0 ] − [ 2 7 7 − 0 ] = 8 − 4 + 128 3 − 128 7 = 84 + 896 − 384 21 = 596 21 Thus, the value of the given iterated integral is 596 21 . Use online graphing calculator to sketch the graph of x 3 ≤ y ≤ 4 x , 0 ≤ x ≤ 2 as shown in below Figure 1. From Figure 1, it is observed that the shaded region is R . From the definition of regular x region it is clear that, the below defined order of integration indicates that the region is regular x region. That is, R = { ( x , y ) | x 3 ≤ y ≤ 4 x , 0 ≤ x ≤ 2 } . From the definition of regular y region it is clear that, the below defined order of integration indicates that the region is regular y region. That is, R = { ( x , y ) | y 4 ≤ x ≤ y 3 , 0 ≤ y ≤ 8 }

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14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 14.7, Problem 36E

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To evaluate: The integral ∫02[∫x34x(1+2y)dy]dx and graph the region of integration, then reverse the order of the integration and do the same.

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Chapter 14.7, Problem 35E

Chapter 14.7, Problem 37E

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Note: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…

4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.024. Find the approximations Tη, Mn, and S, to the integral computer algebra system.) ASK YOUR TEACHER PRACTICE ANOTHER 4 39 √ dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a n Tn Mn Sp 6 12 n ET EM Es 6 12 What observations can you make? In particular, what happens to the errors when n is doubled? As n is doubled, ET and EM are decreased by a factor of about Need Help? Read It ' and Es is decreased by a factor of about

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Chapter 14 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Prob. 5MP Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

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The integral ∫ 0 2 [ ∫ x 3 4 x ( 1 + 2 y ) d y ] d x and graph the region of integration , then reverse the order of the integration and do the same.

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To evaluate: The integral ∫02[∫x34x(1+2y)dy]dx and graph the region of integration, then reverse the order of the integration and do the same.

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Chapter 14 Solutions