a. Explanation Given: The integral is given by ∫ 0 4 ( 3 x + 2 ) 2 d x Calculation: Let’s take Δ x = b − a n = 4 − 0 n = 4 n and x i = 4 i n The n-rectangle left sum for f on [0,4] is ∑ i = 1 n f ( x i ) Δ x = ∑ i = 1 n f ( 4 i n ) Δ x = ∑ i = 1 n ( 3 ( 4 i n ) + 2 ) 2 ( 1 n ) b. To determine The integral. c. To determine The integral using the Fundamental theorem of Calculus.

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Question

Chapter 4.5, Problem 14C

To determine

The integral using the limit of Riemann sums.

To determine

The integral.

To determine

The integral using the Fundamental theorem of Calculus.

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Chapter 4.5, Problem 13C

Chapter 4.5, Problem 15C

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EXAMPLE 3 Find S X √√2-2x2 dx. SOLUTION Let u = 2 - 2x². Then du = Χ dx = 2- 2x² = 信 du dx, so x dx = du and u-1/2 du (2√u) + C + C (in terms of x).

Chapter 4 Solutions

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The integral using the limit of Riemann sums.

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The integral using the Fundamental theorem of Calculus.

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Chapter 4 Solutions