(a) Explanation Given: The provided function is: f ( x ) = x 2 Number of rectangles n = 4 and the provided interval is x = 0 to x = 4 . Formula used: Area of the rectangle as: A = ( length ) × ( width ) Calculation: The provided function is: f ( x ) = x 2 Now, find width of each rectangle. Consider the width of the each is B then, B = ( b − a ) n Since, a = 0 , b = 4 and the total number of rectangles is 4 then, Substitute the values in the above expression to find the width of each rectangle then, B = ( b − a ) n = ( 4 − 0 ) 4 = 4 4 = 1 So, the width of each rectangle is 1 unit . Now, find the height of 4 rectangles by substituting x = 0 , 1 , 2 and 3 (b) To determine To calculate: The approximated area of the region over the provided interval. (c) To determine To calculate: The value of ∫ 0 4 x 2 d x using formula of area of triangle.

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

12th Edition

ISBN: 9780134862651

Author: Lial

Publisher: PEARSON

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Question

Chapter 13.4, Problem 16E

(a)

To determine

To calculate: The approximated area of the region over the provided interval.

(b)

To determine

To calculate: The approximated area of the region over the provided interval.

(c)

To determine

To calculate: The value of ∫04x2dx using formula of area of triangle.

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Chapter 13.4, Problem 15E

Chapter 13.4, Problem 17E

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Chapter 13 Solutions

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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