Let g(x) f(z) on [a,b]. P R Let R be the region bounded by y...

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Let g(x) ≤ f(z) on [a,b]. P R Let R be the region bounded by y = f(r), y = g(r), z = a and r= b. Recall that the area of R is given by A-f(x)-g(x)]dx. Then the centroid of R is (F.) where -xf(x) = g(x)}dr. *-*HUOP-9(0)¹1) dr. (1) Use integration to find the center of mass of the triangle (0,0)(2,0)(0.8). (2) Use integration to find the center of mass of the rectangle (1,-3)(4,-3)(4,5)(1,5). (3) Find the center of mass of the I-quadrant portion of the unit circle centered at the origin of radius 1. I= (4) Find the center of mass of the region bounded between the two parabolas: y=-²-2+4 and y=-22²-2r +6. (5) Find the center of mass of the triangle with vertices (a.0), (0.6). (0,c) (a > 0. b> c). How would you verify that your answer is correct? (6) Discuss but do not submit. Give an example of a planar region whose center of mass lies on its boundary. Let g(x) ≤ f(z) on [a,b]. P R Let R be the region bounded by y = f(r), y = g(r), z = a and r= b. Recall that the area of R is given by A-f(x)-g(x)]dx. Then the centroid of R is (F.) where -xf(x) = g(x)}dr. *-*HUOP-9(0)¹1) dr. (1) Use integration to find the center of mass of the triangle (0,0)(2,0)(0.8). (2) Use integration to find the center of mass of the rectangle (1,-3)(4,-3)(4,5)(1,5). (3) Find the center of mass of the I-quadrant portion of the unit circle centered at the origin of radius 1. I= (4) Find the center of mass of the region bounded between the two parabolas: y=-²-2+4 and y=-22²-2r +6. (5) Find the center of mass of the triangle with vertices (a.0), (0.6). (0,c) (a > 0. b> c). How would you verify that your answer is correct? (6) Discuss but do not submit. Give an example of a planar region whose center of mass lies on its boundary.

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