Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 6. Use the equations shown below with 8 = 1 and M = area of the region covered by the plate. b x= = S8 a 8x[f(x)-g(x)] dx b 1 y=[²(x) - 9²(x)] dx a The centroid of the thin plate is (x,y), where x = and y=. (Type integers or simplified fractions)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = − x+6. Use the equations shown below with 8 = 1 and M = area of the region covered by the plate.
X =
1
b
a
8x[f(x) – g(x)] dx
-
b
1
8
y = -√√√ [²(x) - g² (x)] dx
M
a
The centroid of the thin plate is (x,y), where x =
(Type integers or simplified fractions.)
and y=
Transcribed Image Text:Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = − x+6. Use the equations shown below with 8 = 1 and M = area of the region covered by the plate. X = 1 b a 8x[f(x) – g(x)] dx - b 1 8 y = -√√√ [²(x) - g² (x)] dx M a The centroid of the thin plate is (x,y), where x = (Type integers or simplified fractions.) and y=
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