Find the surface area of z=x2+y above the triangle with vertices (0,0),(2,0),(2,2)?

Q: Find the area of the surface x2 - 2 ln x + sqrt(15)y - z = 0 above the square R: 1<=x <= 2,…

A:

Q: Find the area of the “triangular” region in the xy-plane that is bounded on the right by the…

A:

Q: Determine the distance of the centroid from the x-axis for the area bounded by the curves y?=4x, x-0…

A:

Q: Find the centroid (7, ī) of the region bounded by: y = 4x? + 4x, y = 0, x = 0, and x = 1 y= Il

A:

Q: B) Find the area of plate bounded by y =x-1,y =3-x and y 0.

A: The area is the measure of the amount of space occupied by a plane figure. It can be expressed in…

Q: Find the centroid of the region bounded by y² = NOTE: Enter the exact answers. 16x and y² = 32(x −…

A:

Q: Find the centroid (, y) of the region bounded by: y = 6x2 +9x, y 0, a = 0, and x = 1.

A:

Q: Find the area of the plane region bounded by the curves y = Vx - 1, y = 3, the x-axis, and the…

A: Region bounded be the curves is given, we need to find the area of the region. Firstly,  we'll draw…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3x + 3y R:…

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

A:

Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: Find the centroid (¯x,¯y) of the region bounded by: y=8x2+9x,   y=0,   x=0,   and    y=0,   x=0,…

A: Given data: The first function given is f(x)=8x2+9x. The second function given is g(x)=0. The given…

Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

A:

Q: Determine the centroid of the area bounded by the y − axis, the x − axis, and the curve x2+y−4=0.

A: We have given the curve x2+y−4=0 and boundaries x-axis i.e. y=0 and y-axis i.e x=0

Q: The surface area of the surface generated by revolving y=x^3 , 0<=x<=1 about the x-axis is

A: We have to find the surface area of the region generated by y=x^3, 0&lt;=x&lt;=1 about the x-axis. I…

Q: Find the area and centroid bounded by y= 2(1-x^2), y=x^2-1. Graph.

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

A:

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 9 − x2 R:…

A: Find the area of the surface given by z = f (x, y) that lies above the region R.

Q: Find the volume of the solid above the triangle with vertices (0, 0), (1, 0) and (1, 2), below the…

A:

Q: What is the area of the enclosed surface bounded by the x-axis, x = 2 and y=x2 ?

A: The area under the curve can be calculated by the integration. The formula for the integration is…

Q: 10. Find the centroid of the area bounded by the parabolas x 2y and x - 2x - 2y = -5, and y-axis

A:

Q: Find the centroid of the area bounded by the curves y = x^3, x = 0 and y = 8

A:

Q: Find the centroid (x¯,y¯)(x¯,y¯) of the region bounded by: y=7x^2+2x,   y=0,   x=0,   and   x=9?

A:

Q: Find the Area of a Surface of Revolution. y= (x3/6)+(1/2x), 1≤x≤2

A: Given y=f(x)=x36+12x,   1≤x≤2

Q: Find the surface area give y^2 +4x =2lny, 0, 0≤y≤3  ; about the  x-axis.

A: We have to find the surface area give y2 + 4x = 2lny , 0 ≤ y ≤ 3 ,  about the  x-axis.

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: Compute surface area about the x-axis over the interval y= 4-x23 2,[0,8] 2/3 3/2

A:

Q: 2 y=x¯,y= 2x

A: The objective of the question is calculate area of the bounded region .

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) 13 + 9x -3y…

A:

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 3 + 2x3/2…

A: Consider the function. fx,y=3+2x32 The surface area can be calculated as, S=∬R1+fxx,y2+fyx,y2 Now,…

Q: Find the area and centroid bounded by y=-x^2+6, y=x^2+3x. Graph

A:

Q: Find the centroid (x, y) of the isosceles, right triangle whose boundaries are the two coordinate…

A:

Q: Find the centroid along the y-axis of the plane area bounded by the equation y^2=4x, x=1 and the…

A: Given curve is y2=4x ,x=1

Q: Find the area of the region bounded by y = 5-x2, y 2x+2, y=-x-1, a. in terms of x b. in terms of y y…

A: We will find out the required value.

Q: Find the area of the surface z = x^2 − y^2 that sits inside the cylinder x^2 + y^2 = 1

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. 3 + 6x3/2 f(x, y) R:…

A: In this question, we need to find the area of the surface.

Q: Solve the problem. Find the centroid of the region cut from the first quadrant by the line +=1 x =…

A:

Q: Determine the centroid of the area bounded by the y-axis, the x-axis,  and the curve x2 + y − 4 = 0.

A:

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: Find the area of the surface that is obtained by rotating the graph of X = 1+ Y² (Y = 1 to Y= 2)…

A:

Q: Find the centroid (¯x,¯y)of the region bounded by: y=4x2+7x, y=0,   x=0,   and   x=3 ¯x=    ¯y=

A:

Q: Find the Area of a Surface of Revolution. y=1/3(x3), [0,3]

A: Given, y=13x3   interval :0,3

Q: Find the volume of the region above the triangle with vertices (1,0), (0,1) and (3,1), below the…

A: Given Data: fx,y=x2y The vertices of the triangles are (1,0), (0,1) and (3,1).

Q: find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 − x2 R:…

A:

Q: Find the centroid of the semicircular area inside x2+ y2 = a2 with y ≥ 0. Show the graph for it.

A:

Q: Determine the surface area of the part of z = 13 - 4x2 - 4y2 that is above z = 1 with x <1 and y <0.…

A: Surface area:- The total area of all the faces of a three-dimensional object is its surface area. We…

Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: We have to to write in integral form

Q: compute the surface area of revolution about the x-axis over the interval. y = (4 − x2/3)3/2, [0, 8]

A:

Q: Find the area of the surface that is obtained by rotating the graph of X = 1+Y² (Y = 1 to Y= 2)…

A:

Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x

A: The given curves are y=-x+2 and y=x2-2x. The main objective is to find the area of the plane region…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.