Explanation Use the fact that cos x decreases in the interval [ π 8 , π 4 ] and hence cos π 4 ≤ cos x ≤ cos π 8 . Applying integrals to the equation and evaluation gives the required proof. Given: 0.277 ≤ ∫ π / 8 π / 4 cos x d x ≤ 0.363 Calculation: We know that cos x decreases in the interval [ π 8 , π 4 ] . Hence, cos π 4 ≤ cos x ≤ cos π 8 Applying integrals to the above equation ∫ π / 8 π / 4 cos π 4 d x ≤ ∫ π / 8

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 5.2, Problem 78E

To determine

To prove that $0.277 \leq \int_{π / 8}^{π / 4} \cos x d x \leq 0.363$

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Chapter 5.2, Problem 77E

Chapter 5.2, Problem 79E

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