Explanation Given info: The solid in the octant x ≥ 0 , y ≥ 0 , z ≥ 0 , bounded by x + y + z = 1 and x + y + 2 z = 1 Concept used: Volume = ∭ w d v (putting the value of dv) = ∬ D [ ∫ d x ] d y . d z (Rearrangement to integrate with respect to x) Where Disprojection of W over. x y Plane. Calculation: The surface is bounded above by the plane x + y + 2 z = 1 and below by x + y + z = 1 ( as show in figure ) . z . Lies below z = 1 − x − y , and above z = 1 2 ( 1 − x − y ) i . e 1 2 ( 1 − x − y ) ≤ z ≤ ( 1 − x − y ) To find x and y .limit take projection on x y plane of the bounded region i . e x + y = 1 For y − limit element show in figure 0 ≤ y ≤ 1 − x 0 ≤ x ≤ 1 W: 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 − x , 1 2 ( 1 − x − y ) ≤ z ≤ ( 1 − z − y ) Volume = ∭ w d v = ∬ D [ ∫ d x ] d y . d x (Rearrangement to integrate with respect to x) = ∫ 0 1 ∫ 0 1 − x ∫ 1 2 ( 1 − x − y ) ( 1 − x − y ) d z d z d x First integrate with respect to z assuming x and y as constant = ∫ 0 1 ∫ 0 1 − x [ ∫ 1 2 ( 1 − x − y ) ( 1 − x − y ) d z ] d y d x ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.3, Problem 21E

To determine

Find the volume of the solid in the octant $x \geq 0,$ $y \geq 0, z \geq 0,$ bounded by $x + y + z = 1$ and $x + y + 2 z = 1$

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Chapter 16.3, Problem 20E

Chapter 16.3, Problem 22E

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the answer is C, could you show me how to do it

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.1 - Prob. 45E Ch. 16.1 - Prob. 46E Ch. 16.1 - Prob. 47E Ch. 16.1 - Prob. 48E Ch. 16.1 - Prob. 49E Ch. 16.1 - Prob. 50E Ch. 16.1 - Prob. 51E Ch. 16.1 - Prob. 52E Ch. 16.1 - 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Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Prob. 37E Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 44E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Prob. 47E Ch. 16.5 - Prob. 48E Ch. 16.5 - Prob. 49E Ch. 16.5 - 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Prob. 26CRE Ch. 16 - Prob. 27CRE Ch. 16 - Prob. 28CRE Ch. 16 - Prob. 29CRE Ch. 16 - Prob. 30CRE Ch. 16 - Prob. 31CRE Ch. 16 - Prob. 32CRE Ch. 16 - Prob. 33CRE Ch. 16 - Prob. 34CRE Ch. 16 - Prob. 35CRE Ch. 16 - Prob. 36CRE Ch. 16 - Prob. 37CRE Ch. 16 - Prob. 38CRE Ch. 16 - Prob. 39CRE Ch. 16 - Prob. 40CRE Ch. 16 - Prob. 41CRE Ch. 16 - Prob. 42CRE Ch. 16 - Prob. 43CRE Ch. 16 - Prob. 44CRE Ch. 16 - Prob. 45CRE Ch. 16 - Prob. 46CRE Ch. 16 - Prob. 47CRE Ch. 16 - Prob. 48CRE Ch. 16 - Prob. 49CRE Ch. 16 - Prob. 50CRE Ch. 16 - Prob. 51CRE Ch. 16 - Prob. 52CRE Ch. 16 - Prob. 53CRE Ch. 16 - Prob. 54CRE Ch. 16 - Prob. 55CRE Ch. 16 - Prob. 56CRE Ch. 16 - Prob. 57CRE Ch. 16 - Prob. 58CRE Ch. 16 - Prob. 59CRE Ch. 16 - Prob. 60CRE Ch. 16 - Prob. 61CRE

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Find the volume of the solid in the octant x ≥ 0 , y ≥ 0 , z ≥ 0 , bounded by x + y + z = 1 and x + y + 2 z = 1

Solution Summary: The author calculates the volume of the solid in the octant x 0, y

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Find the volume of the solid in the octant $x \geq 0,$ $y \geq 0, z \geq 0,$ bounded by $x + y + z = 1$ and $x + y + 2 z = 1$

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Chapter 16 Solutions

Find the volume of the solid in the octant x ≥ 0 , y ≥ 0 , z ≥ 0 , bounded by x + y + z = 1 and x + y + 2 z = 1

Solution Summary: The author calculates the volume of the solid in the octant x 0, y

Videos

Find the volume of the solid in the octant x≥0,y≥0,z≥0, bounded by x+y+z=1 and x+y+2z=1

Want to see the full answer?

Chapter 16 Solutions

Find the volume of the solid in the octant $x \geq 0,$ $y \geq 0, z \geq 0,$ bounded by $x + y + z = 1$ and $x + y + 2 z = 1$