Explanation Given: The given integral is ∫ 0 π f ( x ) d x . Where the function f ( x ) is given by f ( x ) = { cos x for 0 ≤ x < π 2 x for π 2 ≤ x ≤ π Formula used: Sub-division Property of definite integral: ∫ a b f ( x ) d x = ∫ a c f ( x ) d x + ∫ c b f ( x ) d x Where c ∈ [ a , b ] Calculation: Consider the function. f ( x ) = { cos x for 0 ≤ x < π 2 x for π 2 ≤ x ≤ π Consider the integral ∫ 0 π f ( x ) d x

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 5.4, Problem 52PS

To determine

To find: The value of the integral ∫0πf(x)dx .

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Chapter 5.4, Problem 51PS

Chapter 5.4, Problem 53PS

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17. Consider a mass-spring system that satisfies 2y′′(t) + by′(t) + 50y(t) = 0.Which of the following is/are true?(i) If b = 0, the motion is critically damped with period π/5 .(ii) If b = 12, the motion is underdamped.(iii) If b = 40, the motion is overdamped.A. (ii) and (iii) only B. (ii) only C. (i) and (ii) only D. (i) and (iii) only E. All

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Chapter 5 Solutions

Calculus

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The value of the integral ∫ 0 π f ( x ) d x .

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Chapter 5 Solutions