Explanation Calculation: (a) Consider the function f x = sin x . Calculate the left end point approximation. Now, consider the interval 0 , π 2 . For n = 10 , Δ x = π 2 − 0 10 = π 20 = 0.16 Find the value of left end point with the help of formula x k * = a + k − 1 Δ x for k = 1 , 2 , 3.... , n . Calculate the area with the help of formula ∑ k = 1 n f x k * Δ x . Using CAS, the value is, A = 0.16 0 + 0.15931821 + 0.31456656... + 0.95801586 + 0.99145835 = 0.91940317 For n = 20 , Δ x = π 2 − 0 20 = π 40 = 0.08 Using CAS, A = 0.08 0 + 0.079914694 + 0.15931821 + ... + 0.59719544 + 0.65938467 = 0.960215997 For n = 50 , Δ x = π 2 − 0 50 = π 100 = 0.31 Using CAS, A = 0.31 0 + 0.30505864 + 0.58103516... + 0.61437426 + 0.34439347 = 0.984209789 (b) Consider the given function f x = sin x . Calculate the midpoint approximation. For n = 10 , Δ x = π 2 − 0 10 = π 20 = 0.6 Find the value of midpoint point with the help of formula x k * = a + k − 1 2 Δ x for k = 1 , 2 , 3.... , n . Calculate the area with the help of formula ∑ k = 1 n f x k * Δ x . Using CAS, A = 0.6 0

11th Edition

ISBN: 8220102011618

Author: Davis

Publisher: YUZU

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Question

Chapter 5.4, Problem 34ES

To determine

To calculate: The area for fx=sinx for 0,π2 the specified interval with n=10,20 and 50 subintervals. Use CAS.

(a) Using the left end point.

(b) Using the mid end point.

(c) Using the right end point.

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Chapter 5.4, Problem 33ES

Chapter 5.4, Problem 35ES

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Chapter 5 Solutions

EBK CALCULUS EARLY TRANSCENDENTALS SING

Ch. 5.1 - Let R denote the region below the graph of fx=1x2...Ch. 5.1 - Suppose that when the area A between the graph of...Ch. 5.1 - The area under the graph of y=x2 over the interval...Ch. 5.1 - Find a formula for the area Ax between the graph...Ch. 5.1 - The area under the graph y=fx over the interval...Ch. 5.1 - Prob. 1ES Ch. 5.1 - Prob. 2ES Ch. 5.1 - Prob. 3ES Ch. 5.1 - Prob. 4ES Ch. 5.1 - Prob. 5ES

Knowledge Booster

The area for f x = sin x for 0 , π 2 the specified interval with n = 10 , 20 and 50 subintervals. Use CAS. (a) Using the left end point. (b) Using the mid end point. (c) Using the right end point.

Solution Summary: The author explains how to calculate the area for f(x)=mathrmsinx using CAS.

To calculate: The area for fx=sinx for 0,π2 the specified interval with n=10,20 and 50 subintervals. Use CAS.

(a) Using the left end point.

(b) Using the mid end point.

(c) Using the right end point.

Want to see the full answer?

Chapter 5 Solutions

The area for f x = sin x for 0 , π 2 the specified interval with n = 10 , 20 and 50 subintervals. Use CAS. (a) Using the left end point. (b) Using the mid end point. (c) Using the right end point.

Solution Summary: The author explains how to calculate the area for f(x)=mathrmsinx using CAS.

To calculate: The area for fx=sinx for 0,π2 the specified interval with n=10,20 and 50 subintervals. Use CAS. (a) Using the left end point. (b) Using the mid end point. (c) Using the right end point.

Want to see the full answer?

Chapter 5 Solutions

To calculate: The area for fx=sinx for 0,π2 the specified interval with n=10,20 and 50 subintervals. Use CAS.

(a) Using the left end point.

(b) Using the mid end point.

(c) Using the right end point.