4. Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2r and y = 3-r². %3D

Q: find the center of mass of a thin plate of constant density d covering the given region. The region…

A: Given: y=2x2-4x and y=2x-x2 Graph:

Q: Find the centroid of the solid formed by revolving about ox the area bounded by y^2=2x and the line…

A:

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above…

A: The volume of the enclosed region under the, hyperbolic paraboloid z = f(x,y) and above the…

Q: Find the volume of the solid that lies under the hyperbolic paraboloid = 3y² – x² + 2 and above the…

A: Integral

Q: Find the centroid of the region with the indicated boundaries: The parabola y² = 4x, the Y-axis,…

A: We use the formula  x=MyM=∫abxfx-gxdx∫abfx-gxdxy=MxM=∫ab12fx2-gx2dx∫abfx-gxdx Now, fx=4, gx=4x, a=0,…

Q: Find the volume under the parabolic cylinder z = x^2 above the region enclosed by the parabola y=…

A:

Q: Find the centroid of the region bounded by the curves. y=1-x2, y=0

A: We Use the Given Curves Find the Centroid. Firstly We Find Required Area and After we find X and Y…

Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? O 0 02 Ο ΝΑ x-coordinate of the…

A: Solution is given below:

Q: parabola

A:

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 2 and above…

A: Given:z=3y2-x2+2 above the rectangle R=-1,1×1,5Formula:V=∬R z dx dy

Q: find the volume of the solid obtained by rotating region B in Figure 13 about the givenaxis. x-axis

A:

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y² - x2 + 2 and above…

A: The volume of the solid that lies under hyperbolic paraboloid is:

Q: Find the volume of the solid under the plane 3x + 2y – z = 0 and above the region enclosed by the…

A:

Q: Find the centroid of the region that is enclosed between: y = x and y = 2 – 2?.

A: Let fx=2-x2, gx=x. Find the intersections. fx=gx2-x2 =x2-x2…

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

Q: Find the centroid of the region bounded by the graphs y = x² and y = 5x + 14. %3D %3D NOTE: Enter…

A:

Q: Find the centroid of the region in the first quadrant bounded by the x-axis, the parabola y2 = 2x,…

A:

Q: 20 4 18 16- 14 12- 10- Y = (x- 2)4 6 - 21 2. 3, 00 4.

A:

Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

A:

Q: 5. Use the shell method to find the volume of an ellipsoid formed when that part of the ellipse x2 +…

A: Given

Q: Find the centroid of the area of the region bounded by the curves y 2x+1; x+y=D7 and x 8?

A: given, curves y=2x+1 , x+y=7 and x=8 claim- find the centroid of the area of the region bounded by…

Q: find the ordinate of the centroid of the region bounded by the parabola y = x^2 and the line y = 2x…

A:

Q: Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O…

A: We need to find centroid of the region.

Q: Find the centroid of the area bounded by the parabolas x = y2 and x2 = -8y

A: The given problem is to find the centroid of the area bounded by the given parabolas. Given…

Q: Find the centroid of the region bounded by the graphs of the following equation y = Va - x. a

A:

Q: :- Find the volume of the solid between y = x+1 which obtained the curves y = (x-1)² and by rotation…

A:

Q: Find the centroid of the region bounded by y? = 22x and y² = 44(x – 11). %3D NOTE: Enter the exact…

A: The centroid coordinates are given by x¯=1A∫Ax dA and y¯=1A∫Ay dA.

Q: Find the centroid of the region in the first quadrant that is bounded above by the lines y = 2x and…

A:

Q: Problem III. For the bounded and shaded region, find the coordinates of the centroid.

A: given two curves y=x2-20 , y=x let fx=x2-20 gx=x it is known that…

Q: 6. Find the volume inside the paraboloid z = 9-x² - y², outside the cylinder x² + y² = 4, above the…

A: Relation between rectangular and polar coordinate  x=rcosθy=r sinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

Q: 7. Find the volume and centroid generated by revolving the given plane area about y^2=4x, x=4; about…

A: Given that - y2 = 4x, x = 4; about x = 4

Q: Find the centroid of the region bounded by the graphs of the given equations. y = 14 – 2², y= 2 – a

A:

Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: Calculate the volume of the solid bounded by the paraboloid z=2−x2−y2 and the conic surface…

A:

Q: Find the centroid of the region bounded by the parabola y=x? and the line y=4.

A:

Q: Find the centroid of the region bound by curves y=cosx,    y=0,        x=0,     x=?/2

A: Here given that two curves equation that is y=cosx and y=0 Limite is given that x=0 to x=π\2 Then we…

Q: Consider the region enclosed by the curves y=2+1 and y= 2z+1: The volume of the solid generated by…

A:

Q: Find the volume of the solid bounded by the ellipsoid 4 = 1 49

A:

Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2…

A:

Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

A:

Q: Find the centroid of the region bounded by the parabola y=x2 and the line y=4.

A:

Q: Find the centroid of the region in the first quadrant bounded by the given curves. y = x?, x = y7…

A:

Q: Consider the plane region bounded by the graph of the ellipse (x/a)2+( y/b)2 = 1 where a > 0 and…

A: Given: To Find: (a). The volume of the ellipsoid formed when the region is revolved around the…

Q: Find the centroid of the region bounded by the graphs y = x2 and y = 5x + 14. NOTE: Enter the exact…

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: ---------------------------------------------------------------- x2+y2-6ax=0…

Q: Find the centroid of the region bounded by the graphs y = x² and y 5x + 14. NOTE: Enter the exact…

A:

Q: Consider the region enclosed by the curves y = r² + 1 and y = 2r + 1: The volume of the solid…

A: Topic- Area Under the Curve

Q: Find the volume V of the solid below the hyperboloid z = 9 - v1+ x2 + y2 and above the following…

A: Consider the hyperboloid z=9-1+x2+y2, where 1≤r≤2 and -π2≤θ≤π2. Convert Cartesian to polar…

Q: 2. Find the volume of the wedge cut from the 1-st octant in R³ by the surface z = 4-1 - y.

A: