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xl: Find the moment of inertia about the x-axis of a thin plate bounded y the curve x = y? and x = 2y – y? if its density at the point (x.y) is (x, y) = y + 1

xl: Find the moment of inertia about the x-axis of a thin plate bounded y the curve x = y? and x = 2y – y? if its density at the point (x.y) is (x, y) = y + 1

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Ex1: Find the moment of inertia about the x-axis of a thin plate bounded by the curve x = y? and x = 2y- y? if its density at the point (x.y) is 8(x, y) = y + 1 Solution: + x = 2y – y? (0,2) x = y? (1,1) (0,0) To find points of intersections: y? = 2y - y? 2y? – 2y = 0 y2 – y = 0 y(y – 1) = 0 y = 0 then x = 0 y = 1 then x = 1 Now to find moment of inertia: Ix = Sla y²8(x,y)dxdy = f, S y v + 1)dxdy Jyz = y³ + y*)[xl; dy =, +)(2y- y2 - y²)dy = S,v³ + y²)2Cy – y²)dy = 2 f,v* – y5 – y² – y*)dy %3D 11 Multiple tegral H.W Find Iy, I,, Rx, Ry, Ro,X and y
Transcribed Image Text:Ex1: Find the moment of inertia about the x-axis of a thin plate bounded by the curve x = y? and x = 2y- y? if its density at the point (x.y) is 8(x, y) = y + 1 Solution: + x = 2y – y? (0,2) x = y? (1,1) (0,0) To find points of intersections: y? = 2y - y? 2y? – 2y = 0 y2 – y = 0 y(y – 1) = 0 y = 0 then x = 0 y = 1 then x = 1 Now to find moment of inertia: Ix = Sla y²8(x,y)dxdy = f, S y v + 1)dxdy Jyz = y³ + y*)[xl; dy =, +)(2y- y2 - y²)dy = S,v³ + y²)2Cy – y²)dy = 2 f,v* – y5 – y² – y*)dy %3D 11 Multiple tegral H.W Find Iy, I,, Rx, Ry, Ro,X and y
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