Find the surface area of the object obtained by rotating y = 1 +. 8x2 , 2

Q: Find the the surface area of of the indicated surface The portion x +3y+z = 6 in the first octant.

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Q: Find the area of one side of the "winding wall" standing orthogonally on the curve y = x², 2sxs4,…

A: Given curve is: y=x2, 2≤x≤4 The curve on the surface fx,y=x+y To find the area of one side of the…

Q: Find the volume of the "island" which has a surface defined by 20 - 2 over the region on which it is…

A: To find the volume of the island whose surface is given by, z=201+x2+y2−2

Q: Determine the area below y = 3 + 2x - x² and above the x-axis

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Q: Find the total surface area of the solid below. Round your answer to the nearest hundredth. x= 20…

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Q: Find the area of the surface. The portion of the cone z = 6Vx2 + y2 inside the cylinder x² + y² = 16

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Q: (b) Find the area enclosed by the curve y = 4x2 and the x-axis between x = -2 and x = 2. %3D

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Q: Find the total area of the region between the curve and the x-axis. 24) y = x2(x- 2)2; 0sxs2 15 A) -…

A: The graph of the bounded region is as shown above. As shown draw a stipe parallel to y-axis. So, y…

Q: Find the area enclosedby the parabola y=x² - 8x+15 and thex-axis.

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Q: What is the area enclosed by the curves y= x° - 8x + 18x- 5 and y = x+ 5? A 10.667 в 11.833 14.583…

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Q: 3. Find the area of the region bounded by the parabola y? = 2x – x and the line y = x – 5 by taking…

A: We have equation of parabola  y2=2x-xy2=x                                                     ……(1)…

Q: Q4/ Find the area of the region enclosed by the curves 4x² + y = 4 and x* - y = 1.

A: Consider  the curves  4x2+y=4x4−y=1

Q: Find the area enclosed by the line y = x – 1 and the parabola y? = 2x + 6.

A: Given: The line is y = x-1 and the parabola is y2=2x+6   To determine: The area enclosed by the line…

Q: Find the area enclosed by the parabola y=x2-8x+15 and the x-axis

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Q: Find the area of the shaded region below. x= y? – 4y (-3, 3) x= 2y – y?

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Q: Find area bounded by the circle x? + y² = 25, the y-axis and the parabola y = 6x – x².

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, the x- axis and the parabola x? -…

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Q: 3. Find the surface area of the object obtained by rotating y = 4 + 3x?, 1<x<2 about the y-axis.

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Q: Find the area of the shaded region.

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Q: Find the area of the shaded region below. у y =Vx 2 x=2 1 y=- x1 Area

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Q: Find the area enclosed by the line y = x – 1 and the parabola y? = 2x + 6. %3D

A: To find the area enclosed by the line y = x - 1 and the given parabola.

Q: The area enclosed by the curves y = x and y = 3x – x² is (a) 2/3 (b) 4/3 (c) 10/4 (d) 9/2 (е) 2

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Q: Find the area under one arch of the trochoid x=10θ−3sin(θ),y=10−3cos(θ). Area =

A: Given X and Y equations We have to differentiate the equations with respect to theta

Q: Find the area inside both curves: r = 3+ 2sine and r = 2

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Q: find the area of the portion of the cylinder x²+z²=16 lying inside the cylinder x²+y²=16

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Q: Q5 / Find the area of the triangular region in the first quadrant bounded by the x-axis and the…

A: We have to solve given problem:

Q: Find the area within the curves y = 25 – x², 256x = 3y², and 16y = 9x %3D %3D

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Q: Find the area bounded by the parabola x² = 4y and y = 4 A. 21.33

A: Solution of the problem as follows

Q: a) Find the area of the curve x²/3 +y2/3 = a²/3 %3D

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Q: Q4/ Find the area of the region enclosed by the curves 4x² + y = 4 and x* – y = 1 . |

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Q: Find the area enclosed by the line x=y and the parabola 4x+y² =12

A: Given:         The line x = y  and the parabola 4x + y2 = 12   To find:           The area…

Q: Find the area of the region that is enclosed between y = 6x² – 2³ + ¤ and y = z² + 5z. The area is

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Q: ind the area between the curves.   x = -2, x = 1, y = 2 x 2 + 4, y = 0

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Q: Determine the area enclosed by the curve r² = 4a²cos3θ a. 4a² b. 8a² c. 16a² d. a²

A: Given: The polar equation r2=4a2cos3θ To find the area enclosed by the curve r2=4a2cos3θ The formula…

Q: Find the area enclosed by the curves y = y = 2 1– 9x2 (A B © i- 3. 2π

A: The area enclosed by the curves,y=11-9x2 and y=2

Q: Find the enclosed area by the curve with equation f (x) = x² – 4 and g (x) = 8 – 2x2 40 35 36 32

A: To find the enclosed area between given two curves.

Q: The area enclosed by the curves y = x + 2 and x is . y = 7 + 5x %3D - .... 1) 36 2) 120 3) 34 4) 118…

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Q: Find the area of the shaded region below. y=Vx+ 2 x = 2 1 y = x+1 Area =

A: Form the definite integration of the difference of the given functions and simplify.

Q: Find the area enclosed by {x=t3/2+t+6 & y=-t2+5t-4} and the x-axis

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Q: Find the area bounded by the curve y=-x³x² + 3x and the line y=x. 16 A 8 square units B 16 square…

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Q: Ə)Find the enclosed R the cnes by -x? + 2x +7 region y =x? - 2X 11 and y=

A: Given curves are y=x2-2x+1 &amp; y=-x2+2x+7 To find the area bounded by them, first of all let us…

Q: Find the area enclosed by the x-axis and the curve y=4 – x2. A 32 square units B 18 square units 32…

A: We have to find the area

Q: Find the area of the shaded region. 12) y = Jx - 3 (16,1) 16 (0, -3)

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Q: Q5/ Find the area of the surface generated by revolving y= where 0sxs 2, about the X-axis.

A: The surface area generated by revolving a curve f(x) over the interval [a,b] about the x-axis:…

Q: 135 Find the area of the surface generated by revolving x = 4V9 - y. 0sys- about the y-axis. 16

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Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

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Q: The radius of gyration of the area shown about the x axis is: Y 4 2. 3.

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

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Q: Find the area of the shaded region below. y A x= y² – 4y (-3, 3)- x = 2y – y?

A: Using the method of Integration

Q: Find the surface area revolve about x-axis at y = x³ from 0 < x< 2 98TT Answer: -sq. units 81

A: The curve y=19x3 from 0≤x≤2 revolved about x-axis.