The region in the first quadrant is bounded by the curve y = 2 - x^2 and y = x^2. How far is the centroid of the curve from the y-axis? * 2/3 1/4 3/8 O 4/9

Q: Case 2. Assume that the function F(uo,..., u4) is non-decreasing in uo,u1 and non-increasing in u2,…

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Q: Find the average height of a hemisphere z=sqr( 4-49x^2-49y^2 ) above the disk x ^2+ y^2 ≤4/49.…

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Q: Find the centroids of the function, y=4x-x^2, y=x (please sketch the graph)

A: Let's find.

Q: Please draw the graph that shows the cross section of the function f(x,y)=2y^3+3y^2−2x+4 and the…

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Q: The area in the third quadrant bounded by the curve x = y^2 + 2y is * -1 1 -1 -3-

A: Recall:  Area bounded by the curves:           The area between the curves y=f(x)  and  y=g(x) on…

Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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Q: Find each of the two areas bounded by the curve y = x³ – 4x and y = x² + 2x. Solve in two ways.

A: Given curves are, and Comparing both,

Q: find the area of the region bounded by the parabola x=y^2+2 and the line y=x-8

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: Find the area bounded by the curve y^2+x-4y=5 and the y-axis.

A: The figure is given below

Q: Find the areas enclosed by the following curves: (b) y = x4 – 4x² + 4_and y = x² y = x? 57 3- y = x*…

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Q: Use 8 rectangles to find the area of the curve for the equation y = -x^2 + 9 on [-3, 3].

A: area=∫abf(x)dx≈∆xf(x0)+f(x1)+...............+f(xn-2)+f(xn-1)                      where, ∆x=b-an

Q: Locate the centroid of the parabola by integration

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Q: graph and find the area of the loop bounded by the curve a^3y^2 = x^2 (a-x)^3

A: The given curve is a3y2=x2a-x3y2=x2a-x3a3y=x2a-x3a3y=xaaa-x3 The graph is shown below.