Explanation Given : The graphs of x = sin y and x = 1 − cos y are given as shown. Formula used : Area bounded by two curves is calculated using the formula as given below, A r e a = ∫ a b ( C u r v e t o t h e r i g h t – C u r v e t o t h e l e f t ) d y Calculation : If we look carefully, when 0 ≤ y ≤ Π 2 the curve x = sin y is the one at the right and x = 1 − cos y is at the left, and when − Π 2 ≤ y ≤ Π 2 , curve x = 1 − cos y is at the right and x = sin y is at the left. Therefore, area bounded by the two curves is given by ∫ − Π 2 0 ( ( 1 − cos y ) − sin y ) d y + ∫ 0 Π 2 ( sin y − ( 1 − cos y ) ) d y Simplifying the above expression, we get, ∫ − Π 2 0 ( 1 − cos y − sin y ) d y + ∫ 0 Π 2 ( sin y + cos y − 1 ) d y Integrating above expression to get the area bounded, we get =

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

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Question

Chapter 6.1, Problem 22E

To determine

The area under two curves $x = \sin y$ and $x = 1 - \cos y$ when $- \frac{Π}{2} \leq y \leq \frac{Π}{2}$ .

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Chapter 6.1, Problem 21E

Chapter 6.1, Problem 23E

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Chapter 6 Solutions

CALCULUS (CLOTH)

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The area under two curves x = sin y and x = 1 − cos y when − Π 2 ≤ y ≤ Π 2 .

Solution Summary: The author explains the formula used to calculate the area bounded by two curves.

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The area under two curves $x = \sin y$ and $x = 1 - \cos y$ when $- \frac{Π}{2} \leq y \leq \frac{Π}{2}$ .

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Chapter 6 Solutions

The area under two curves x = sin y and x = 1 − cos y when − Π 2 ≤ y ≤ Π 2 .

Solution Summary: The author explains the formula used to calculate the area bounded by two curves.

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The area under two curves $x = \sin y$ and $x = 1 - \cos y$ when $- \frac{Π}{2} \leq y \leq \frac{Π}{2}$ .