Find the surface area of the part of the surface z=x^2+3y that lies above the triangular region T in the xy-plane with the vertices (0, 0), (1, 0), and (1, 12). Give your answer in 2 decimal places. You have to use the following formula:

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

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Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Find the surface area of the solid obtained by y=2x, 0sx58revolving around the x-axis

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

A:

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z > 0, by the cylinder x2 + y2 = 2y

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³.

A:

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

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Q: Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

A:

Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: Find the surface area for the object obtained by rotating y=7x+2 about the x-axis over the interval…

A:

Q: Calculate the surface area of the z=x²+y surface on the triangular region with vertices (0,0), (1,0)…

A: Let z=fx,y. Differentiate the function fx,y with respect to x and y, to obtain fxx,y and fyx,y.…

Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

A:

Q: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: Find the centroid of the region bounded by y = 28x and y = 56 (x – 14). Enter the exact answer as a…

A: Given: The regions bounded by y2 = 28x  and y2 = 56(x-14). To determine: The Centroid of the region…

Q: Find the area of the surface formed by revolving the graph of f (x) = x³ on the interval [0,1]…

A:

Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

A:

Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

Q: Find

A:

Q: find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x…

A: The triangular plate is bounded by y-axis, y=x,y=2-x if ∂x,y=6x+3y+3. Thus, the region is…

Q: The area of the surface obtained by rotating the curve y = V16 – x² -1 <x< 1, about the x- axis is

A: The given function is y=16-x2 , -1≤x≤1 rotating the curve about x-axis.

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A:

Q: Find the area of the surface obtained by rotating the curve y = √(5-x),   3≤x≤5 about the x-axis.

A:

Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

A:

Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

A:

Q: The area of the surface obtained by rotating the curve y = 17 x +1, 0SXS 34 about the x-axis is

A: The solution are next step...

Q: y = N|XW --- - 6x 1 <x<1

A:

Q: 7 Find the area of the surface generated by revolving x = 2/4-y, 0sys about the y-axis.

A:

Q: Find the area of the surface formed by revolving the graph of y = Vx + 2 on the interval [1,8] about…

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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 surface generated by revolving the curve Y = 8/x, 2 < x < 7 around the -axis.

A: The given surface is generated by y=8x,  2≤x≤7 around the x axis. The area of the surface generated…

Q: f(x) = x², with 0< y < 4

A:

Q: Find the area of the part of the surface ¤= (y/2 + z3/2) with y E [0, 2] and z E [0, 2]. Area =

A: For the solution of the problem follow the next step.

Q: Find the area of the surface generated by revolving the curve y =2x-x, 0.5sxs1, about the x-axis.

A: To calculate the area of the surface we use the formula A=2π∫abf(x)1+((f'(x))2 dx

Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

A:

Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

Q: Use Pappus’s Theorem for surface area and the fact that the sur-face area of a sphere of radius a is…

A:

Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

A:

Q: Find the area of the surface that is generated by revolving the curve y= V16 – x² on the interval…

A:

Q: x = 1+ 2y2, 1< x < 2 about the x-axis.

A:

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

A:

Q: Find the centroid of the region bounded by the curves y = 2x3 – 2x and y = 2x2 – 2. Sketch the…

A: Consider the given curves y = 2x3 – 2x and y = 2x2 – 2

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: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: 9. Find the area of the surface obtained by rotating the curve y = x',0sxs2 about the x-axis.

A: Given : y = x³, 0≤x≤2 about the x-axis

Q: Find the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

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 surface area obtained by rotating y = V9 – x² -2sxs-1

A: As we know that; The expression for the area of surface rotating about the x-axis. S=2π∫abfxf'x2+1dx…

Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3