Explanation Find the value of Δ x and using the formula of R N = Δ x ∑ j = 1 N f ( x j ) and S N = Δ x ∑ j = 1 N f ( x j ) to determine the value of ∫ 0 b x k d x Given: k and b are positive Calculation: Since k and b are positive numbers and assuming f ( x ) = x k on [ 0 , b ] . Δ x = ( b − 0 ) / N = b / N where N is a positive integer. The right-end points of the N subintervals of [ 0 , b ] can be given by x j = a + j Δ x = b j / N , where j = 1 , 2 , 3 , ... , N . Therefore the right-end point approximation to ∫ 0 b f ( x ) d x = ∫ 0 b x k d x is given by R N = Δ x ∑ j = 1 N f ( x j ) = b N ∑ j = 1 N ( b j N ) k = b

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 5.2, Problem 85E

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To prove that $\int_{0}^{b} x^{k} d x = b^{k + 1} \int_{0}^{1} x^{k} d x$ by comparing the right-end point approximations

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Chapter 5.2, Problem 84E

Chapter 5.2, Problem 86E

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5. mit answer urces Use Simpson's Rule and all the data in the following table to estimate the value of the 31 integral f(x) dx. 25 25 26 27 28 29 30 31 f(x) 4 44 4 -9 -2 9 2 5 (Round your answer to within two decimal places if necessary, but do not round until your final computation.) Simpson's Rule Approximation: PROGRES Score Completi 30 i Submit answer T The Weather Channel UP DELL FB F4 F5 F9 9. F10

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To prove that ∫ 0 b x k d x = b k + 1 ∫ 0 1 x k d x by comparing the right-end point approximations

Solution Summary: The author explains how the right-end point approximation to 0 b x k d is given by the formula of R N and S N.

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To prove that $\int_{0}^{b} x^{k} d x = b^{k + 1} \int_{0}^{1} x^{k} d x$ by comparing the right-end point approximations

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To prove that ∫ 0 b x k d x = b k + 1 ∫ 0 1 x k d x by comparing the right-end point approximations

Solution Summary: The author explains how the right-end point approximation to 0 b x k d is given by the formula of R N and S N.

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To prove that ∫0bxkdx=bk+1∫01xkdx by comparing the right-end point approximations

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To prove that $\int_{0}^{b} x^{k} d x = b^{k + 1} \int_{0}^{1} x^{k} d x$ by comparing the right-end point approximations