Explanation Given: The surface is given by f ( x , y ) = 2 x − 3 y + 15 , above the region R , which is rectangular with vertices ( 0 , 0 ) , ( 3 , 0 ) , ( 0 , 3 ) , ( 3 , 3 ) Formula used: The surface area can be calculated of the region R by, S = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 d A Differentiation formula d d x ( x n ) = n x n − 1 , d d x ( constant ) = 0 . Calculation: The function given is f ( x , y ) = 2 x − 3 y + 15 . Now partially differentiating it with respect to x , and use d d x ( x n ) = n x n − 1 , d d x ( constant ) = 0 . f x ( x , y ) = d d x ( 2 x − 3 y + 15 ) = 2 x 1 − 1 + 0 + 0 = 2 Now, with respect to y . f y ( x , y ) = d d y ( 2 x − 3 y + 15 ) = 0 − 3 y 1 − 1 + 0 = − 3 Substitute the above-obtained value in the formula S = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 d A

Calculus: Early Transcendental Functions (MindTap Course List)

6th Edition

ISBN: 9781285774770

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.5, Problem 2E

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To calculate: The area of the surface given by z=f(x,y)=2x−3y+15 which lies above the region R, which is rectangular with vertices (0,0),(3,0),(0,3),(3,3)

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Chapter 14.5, Problem 1E

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Chapter 14 Solutions

Calculus: Early Transcendental Functions (MindTap Course List)

Ch. 14.1 - Evaluate the iterated integral: 0433cosrdrd Ch. 14.1 - Prob. 1E Ch. 14.1 - Evaluate the integral: xx2yxdy Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Evaluate the integral: 04x2x2ydy Ch. 14.1 - Evaluate the integral: x3x(x2+3y2)dy Ch. 14.1 - Evaluate the integral: eyyylnxxdx;y0 Ch. 14.1 - Evaluate the integral: 1y21y2(x2+y2)dx Ch. 14.1 - Evaluate the integral: 0x2yeyxdy

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The area of the surface given by z = f ( x , y ) = 2 x − 3 y + 15 which lies above the region R , which is rectangular with vertices ( 0 , 0 ) , ( 3 , 0 ) , ( 0 , 3 ) , ( 3 , 3 )

Solution Summary: The author calculates the surface area of the region R by z=f(x,y)=2x-3y+15.

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To calculate: The area of the surface given by z=f(x,y)=2x−3y+15 which lies above the region R, which is rectangular with vertices (0,0),(3,0),(0,3),(3,3)

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Chapter 14 Solutions