Explanation Given: The given function is y = sin x + cos x . 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 ∫ sin a x d x and ∫ cos a x d x is shown below. ∫ sin a x d x = − cos a x a + C ∫ cos a x d x = sin a x a + C Calculation: Given, f ( x ) = sin x + cos x

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 30PS

To determine

To find: The area under the curve y=sinx+cosx on [0,π2] .

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Chapter 5.4, Problem 29PS

Chapter 5.4, Problem 31PS

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Chapter 5 Solutions

Calculus

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The area under the curve y = sin x + cos x on [ 0 , π 2 ] .

Solution Summary: The function y=f(x) and the formula to evaluate the integral are shown below.

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To find: The area under the curve y=sinx+cosx on [0,π2] .

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Chapter 5 Solutions