Exercise (b) the centroid of the region bounded by the graphs of the equations Step 1 The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = x. y=sin(x) b $ ax The area of the representative rectangle is dA = (sin x So, the area of the entire region is A = For the above region, f(x)=sin x g(x) = 0 a = 0,b= Therefore, Let Use integration by parts. Let u= -cos x Step 2 The x-coordinate of the centroid for a region of constant density is x=x[rx) - 9(x)] dx. V= Using integration by parts Therefore, Sudv=uv - [vdu. Differentiate with respect to x on both sides. du - dx * - ** x= ✓ dv = sin x dx. Integrate with respect to x on both sides. x sin x dx --x テー ✓ sin (r) dx. -x cos x + Isin x dx -cos(r) 2 2 -[-x cos x + * cos x dx] x sin x dx. 1] The x-coordinate of the centroid of the region is
Exercise (b) the centroid of the region bounded by the graphs of the equations Step 1 The region is bounded by the graphs of the equations y = sin x, y = 0, x = 0, and x = x. y=sin(x) b $ ax The area of the representative rectangle is dA = (sin x So, the area of the entire region is A = For the above region, f(x)=sin x g(x) = 0 a = 0,b= Therefore, Let Use integration by parts. Let u= -cos x Step 2 The x-coordinate of the centroid for a region of constant density is x=x[rx) - 9(x)] dx. V= Using integration by parts Therefore, Sudv=uv - [vdu. Differentiate with respect to x on both sides. du - dx * - ** x= ✓ dv = sin x dx. Integrate with respect to x on both sides. x sin x dx --x テー ✓ sin (r) dx. -x cos x + Isin x dx -cos(r) 2 2 -[-x cos x + * cos x dx] x sin x dx. 1] The x-coordinate of the centroid of the region is
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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