(a) To determine Form an integral for the surface area generated by revolving the curve about x axis. Explanation Given information: The curve function is x y = 1 . The interval is 1 ≤ y ≤ 2 . Revolution about y axis: If x = g ( y ) ≥ 0 is continuously differentiable on [ c , d ] the area of the surface generated by revolving the graph of x = g ( y ) about the y axis is S = ∫ c d 2 π x 1 + ( d x d y ) 2 d y Calculation: Show the curve Equation as follows: x y = 1 x = 1 y (1) Differentiate Equation (1) with respect to y . d x d y = d d y ( 1 y ) = − 1 y 2 Take square on both sides. ( d x d y ) 2 = 1 y 4 Set up an integral for the area of the surface as shown below: S = ∫ c d 2 π x 1 + (b) To determine Sketch the graph for the function x y = 1 . (c) To determine Calculate the surface area numerically by using integral evaluator.

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 6.4, Problem 3E

(a)

To determine

Form an integral for the surface area generated by revolving the curve about x axis.

(b)

To determine

Sketch the graph for the function xy=1.

(c)

To determine

Calculate the surface area numerically by using integral evaluator.

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Chapter 6.4, Problem 2E

Chapter 6.4, Problem 4E

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