Explanation Given: The given function is y = 2 1 + t 2 . Concept used: The area bounded by the x axis and the function y = f ( x ) on [ a , b ] is given by ∫ a b f ( x ) d x . Formula used: Fundamental theorem of Calculus I: ∫ a b f ( x ) d x = F ( b ) − F ( a ) Where F ′ ( x ) = f ( x ) Linear property of integral are as follows: ∫ [ a f ( x ) ± b g ( x ) ] d x = a ∫ f ( x ) d x ± b ∫ g ( x ) d x Formula to evaluate the integral of the form ∫ a x n d x is shown below. ∫ a x n d x = a ∫ x n d x = a x n + 1 n + 1 + C , n ≠ − 1 Formula to evaluate the integral of the form ∫ d x x is shown below

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 5.4, Problem 34PS

To determine

To find: The area under the curve y=21+t2 on [0,1] .

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Chapter 5.4, Problem 33PS

Chapter 5.4, Problem 35PS

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Chapter 5 Solutions

Calculus

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The area under the curve y = 2 1 + t 2 on [ 0 , 1 ] .

Solution Summary: The author explains how to find the area under the curve y=21+t2. The required area is 4.58

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To find: The area under the curve y=21+t2 on [0,1] .

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Chapter 5 Solutions