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12345 [234]
2 years ago
6

Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y =

4x; about the y-axis v = incorrect: your answer is incorrect.
Physics
1 answer:
Simora [160]2 years ago
4 0

The correct answer for  the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, y = 4x is 128/3 * π.

Volume of Solid of Revolution by Shell method is given by

V = 2π * integrate x(height) dx Here, height = 4x-x2

(1)& x-varies from x = 0 to x = 4 then from eqn(1)  V = 2π * integrate x(4x - x ^ 2) dx from x = 0 to 4 = 2π * integrate (4x ^ 2 - x ^ 3) dx from x = 0 to 4

Basic Rule(1) ∫ x^n dx =x^ n+1/ n+1

V=2 π [4((x ^ 3)/3) - (x ^ 4)/4] 0 ^ 4 =2 π[ 4/3 x^ 3 - x^ 4/4 ] 0 ^ 4

V = 2π [4/3 * 4 ^ 3 - (4 ^ 4)/4} - 0]

V = 128/3 * π.

Learn more about area under curve here :-

brainly.com/question/15122151

#SPJ4

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Newton's first law states that objects in motion stay in motion until an unbalanced force is acted upon it is a good fact. When I first personally heard of it in class I had no clue but when I researched it I learned that one good example of this would be those cradle balls and if u swing it, it will keep constantly hitting each other back and fourth over and over until someone grabs it and stops it, so that's what objects in motion stays in motion until an unbalanced force is acted upon it means, because the balls are in motion by moving left to right constantly and its staying in motion by not stopping and that unbalanced force is someone or something maybe hitting it or knocking it over could stop it, balanced means staying still and equal, unbalanced means unstill so moving, the cradle balls are KE and PE, (Kinect and potential energy) because kinetic means moving, so the balls are moving, and potential means stored up, so before u even swing u have the potential energy to swing it different ways before it becomes kinetic. That's one of my favorite examples of Newton's first law and I left you a pic below of cradle balls to help you get the idea.

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