A thin plate in the shape of a lamina occupies the region bounded by the graphs of y = x² and x = 4y². The plate has a constant density of p = 20- gm cm². Sketch the region, and then find both the mass of the plate, and the center of mass of the plate. Set up an integral for each value and then integrate (Show each step). Then evaluate at the limits using the Fundamental Theorem of Calculus. For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places.

Q: i) ii) The following two functions are given: y = x and y = x¹. Sketch the two curves on the same…

A: Topic = Application of integration

Q: 5 (b). ( the base radius making the surface area minimum. ) Consider a cylinder having fixed volume.…

A: Given a cylinder having fixed volume.

Q: 3]. , Let V = ar²h, where V the volume of a right circular cone of radiusr and height h. Show that…

A:

Q: 1. Find the intersections between the curve y=√√3-x and line y+1-x=0 (a) Sketch the region R bounded…

A:

Q: Consider the function f(x)=1/x on the interval x>=1. find the Surface area and volume of the solid…

A:

Q: Find the volume of a right circular cone with base radius r unites and height h units using the…

A:

Q: D. Calculate volume enclosed by (z = 8-x² - y²) and (z = x² + y²), (Use order dy dz dx). وكنت طول

A: Given

Q: Find the area between the curve y = 2x(x+2) and the line y = -2x. Find the area between the curve y²…

A: Since you have posted multiple questions we could answer first one as per the policy.Please repost…

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

A: To find the center of mass.

Q: Rotate the function 1/x about the x axis from 1 to infinity. a) Does the resulting solid have a…

A: Given f(x) = 1/x

Q: The boundary of a lamina consists of the semicircles y=√16-x² and y= √36-x2 together with the…

A: Here we have to find the centre of the mass of the lamina.

Q: (4,3) Co,o)

A: Answer

Q: enclosed by the Curve Find the area X = 2y² and x = 8

A:

Q: A water reservoir has the shape of a right circular cone with its circular base of radius R = 160 m…

A: General formula for volume of cone, V= (Pi* R^2 * H)/3

Q: 2) Find the area between the two curves y = 10 x² and y = -x + 8. Hint: First find the points where…

A: The given curve is: y=10-x2       ....1y=-x+8      .....2

Q: Find the area of the region enclosed by the curves y = sinx, y = cos x, x = 0 and x = 2n.

A:

Q: The curves y = 2x - x 2 and y = 3x2 - 6x are used to form the boundary of a thin plate of uniform…

A:

Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.