1) Find the area of the surface generated by rotating the function y=x^3 about the x-axis over 0≤x≤3  2) Find the area of the surface generated by rotating the function g(y) = (9-y^2) ^1/2 about the y-axis over 0≤y≤2.

Q: Find the area of the reglon bounded by the graphs of the equations. y = -x+ Bx, y = 0

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Q: 2. Find the cerntroid of the area bounded by the curve y= 2x + 1 x+y =7 and x= 8

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Q: Find the area bounded by the curves 5y^2 = 16x and the curve y^2 = 8x – 24

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Q: Find the area bounded by the following curve and line: y=4/x , y²-4y+2x=5 and the line y=4

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Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x-…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: If a rectangle has its base on the r-axis and two vertices on the curve y = e-", show that the…

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Q: what is the limited area between x = 4y^2-3 and y^2 = x curve Br^2?

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Q: Sketch the region bounded by the graphs of the functions. y = x2 – 8x + 16, y = x2 – 24x + 144, y =…

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Q: 6. Find the area bounded by the curve 2y² + 4x + y = 0 and the line y = 2x.

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Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its…

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: Find the area of the region between the line y = 2x and the curve y = x²+ x – 2

A: y=2x --------(1) y=x2+x-2 -------(2) For points of intersection…

Q: x = y² and the line y = x − 2

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Q: 2. The area bounded by y=3x+4 and the curve y=x2 is revolved about the line x =5.

A: 2) The area bounded by the given curves is:

Q: 2. Find the area bounded by the two curves y=x²-6x²+ 8x and y = x² - 4x.

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Q: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: he area bounded by y^2=4x and the line 4x-3y-4=0.

A: In this question, the concept of Integration is applied to determine the area bounded by two curves.…

Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

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Q: 2. Find the area bounded by the two curves y = x² - 6x²+ 8x and y = x² - 4x.

A: We have to compute the area between the given curves using the double integration method by first…

Q: What is the area of the region between y3Dx^2-2x-3 and the x-axis from x-D0 to x-6?

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Q: The area bounded by the curve z = y.y-axis and the lines Y3D0. y32 is s

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Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

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Q: The area of region bounded by the parabola y2 = 4x and the line %3D y = 2x – 4 is

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4 .

Q: 1. Find the area between the curves x2-y = 9 and the line y 2x-6

A: Since you have posted multiple questions in this question which are not interlinked so I do only…

Q: Given y = 3x –- 2x +1, y =-x² + 2x +1 and a straight line y = 0.5x ; where x>0, 1. Sketch the curves…

A: Given y=3x3-2x2+1  , y=-x2+2x+1 and a straight line y=0.5x. We need to : 1) Sketch the curves and…

Q: The area of the region bounded above by yx+7. bounded below by vey2, bounded from the left by x2 and…

A: The given region is as shown. Now, It is bounded above by y=x+7 and below by y=x2. So, the upper…

Q: 1. Find the area between the curves x2-y2 = 9 and the line y = 2x-6

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Q: Determine the area bounded by: y2-12y-8x+28=0; and x2-4x+4y-20=0

A: The given equations: This can be rewritten as, To find the area bounded by the above equations:…

Q: Find the area of the region enclosed between the curves defined by the equations y = x² – 2x + 2 and…

A: Solve the following

Q: Compute the area contained between the parabolas y and y 3 = 4 --x2

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Q: How do I find the area of the region in the first quandrant bounded by the line y=4x, the line x=4,…

A: Here we have to find the area of the region in the first quadrant bounded by the line y=4x, the line…

Q: 1. Find the area of the region bounded by the curves y = x2 – 3x + 5 and y = 3x + 5.

A: Answer and explanation is given below.. For solution of other questions please repost

Q: Sketch the region bounded by the graphs of the functions. y = x2 - 4x + 4, y = x2 - 12x + 36, y = 0

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Q: 2. Find the area between the curves. x = - 2, x = 1, y = 6x, y = x2 - 7

A: Given: x=-2,x=1,y=6x,y=x2-7

Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

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 finite region bounded by the curve y = 12 + x - x2 and the line: y = x + 3.

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Q: Find the area of the region lying to the right of x = y2 - 5 and to theleft of x = 3 - y2.

A: Given: f(y)=y2-5 and g(y)=3-y2 To find: Where the curve intersect and it is calculated when…

Q: 4. Find the area of the region bounded by the curves x-y² = 0 and x+2y² = 6.

A: Hence, the area of the region bounded by the curves x-y2=0 and x+2y2=6 is 82 square units .

Q: Find the area of the region between the line y = 2x and the curve y = x2 + x − 2

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Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y – 3 = 0. - -

A: Graphically: Now, the area can be found as the following.…

Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

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Q: Find the area between the curve y = 2x² + 4x-6 and the x-axis from x = -2 to x= 3. %3D %3D %3D

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Q: The area under the curve y = 7x bounded by the lines x = 4 and x = 8 above the x – axis is O 336.00…

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Q: 3 2. Find the area bounded by the two curves y = x³- 6x² + 8x and y = x² - 4x.

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Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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Q: Find the area of a triangle bounded by the yy-axis, the line f(x)=10−2xf(x)=10−2x, and the line…

A: Now, from the graph we have the points of intersection of the lines

Q: While evaluating the area of the region bounded by two curves V/y = x and y – 10x + 21 = 0, the -…

A: We will find interesting points.