Find the volume when the area in y = 2x^2 − 8x + 12 and y = −2x + 12 is 9 sq units and revolves around the y axis

Q: Find the area bounded by the parabola y2 − 3x + 3 = 0 and the line x = 4. With illustrations please

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Q: Calculate the total area of the region bounded by the line y= 6x^2 + 9, the x-axis and the line x =4…

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Q: Find the equation of the vertical line that divides the area of the region R bounded by 1 y = 20x2…

A: Identify the limits of integration from the given region, to calculate the area of the region. Here,…

Q: y= -x² + 9; 0 sxs5 x< + 9; 0 < x< 5

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Q: The region bounded by y=√(5-x), x=1, and y=0 is revolved around the (a) x-axis and the (b) y-axis.…

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Q: Write 2 integrals for volume of revolution about x axis  using washer method for region bounded by…

A: By using volume of a solid formula, we calculate the required volume.

Q: Find the volume bounded by: x² + y² + z = 16 and z-x² - y² = 8

A: Concept: If a solid S is bounded by a surface, as in rectangular coordinates,  z=f(r,θ) as well as…

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

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Q: Find the area between the curves. x = 0, x = 6, y = 5x, y = 3x + 10

A: Given: The curves x=0, x=6, y=5x, and y=3x+10 . The bounded area between the given curves is shown…

Q: The graphs of y = 1 − x2 and y = x4 − 2x2 + 1 intersect at three points. However, the area between…

A: Given curves  y=1-x2 y=x4-2 x2+1 Graph :

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

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Q: Determine the area bounded by the curves y = -x – 18x + 40 and y = (x - 2)2

A: The x coordinates for the points of intersection of the curves are given by:…

Q: What is the area of the region between the graps y = x – 1 and line y = -x – 1

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Q: What is the area between y = 0, y = 3x2, x=0, x = 2?

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Q: Find the volume generated if the area bounded by the curve x2 = y - 2 is revolved about the x –…

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Q: Find the area of the region bounded by y = 10x + 4, y = -10x + 3 and x = 14. Leave your answer…

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Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

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Q: Find the volume of a right circular cone with height 18 and base radius 9 using integration.

A: Take a cross-section area of thickness dx at a distance x from top, integrate it from 0 to 18.

Q: Find the volume of the area bounded by the line y = 3x + 4 and the curve y = x² if it is revolved…

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Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: Find the volume of the solid formed by rotating the area between the square with a side length of 2…

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Q: ut the line x = 3.

A: The parabola equation is given , x2 = 4y. The equation of line is given , x = 4 - 2y. The volume…

Q: What is the area bounded by the curves x = 1/y, 2x - y = 0, x = 6, and the x-axis?

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Q: Find the dimensions of the right circular cylinder of maximum volume that can be inscribed in a…

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Q: ded by the curve or line: y2+4x-8=0, Y

A: Given that: The equation of the curve y2 + 4x - 8 = 0. The equation of the line y = 2x.

Q: Find the total area of the shaded region. 1.5- *-5y3 1- (5,1) x= 5y2 0.5- 2.5 7.5

A: Solution

Q: A 6-inch-tall plastic cup is shaped like a surface obtained by rotating a line segment in the first…

A: Given: A 6-inch-tall plastic cup is shaped like a surface obtained by rotating a line segment in the…

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is…

A: Recall: Formula for volume,    V=π∫ab(radius)2dy Given,  y2=12x Substitute x=3 in the above…

Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: The area on the first quadrant of the circle x^2 + y^2 = 36 is revolved about the line y + 10 = 0.…

A: To find: The volume generated by the area on the first quadrant of the circle x2+y2=36 is revolved…

Q: find the area enclosed by the graphs in two ways: by integrating along the x-axis and by integrating…

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Q: Sketch the graph. Set up (DO Not Evaluate) an integral for the volume of the solid that results when…

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Q: Find the area between the curve y = 9 − (x/2)^2 and the line y = 6 − x.

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Q: Find the total area of the region enclosed between the curves: 10x² +24x and =-x³ +10x² 24x

A: The objective is to find the area bounded between the curves.

Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

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Q: Find the area between the curves. x = - 2 , x = 1 , y = 3x , y = x 2 - 4.

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Q: Find the area enclosed by the curves x = -2, x = 3, y = 3x2 - 70, and y = 12x + 26.

A: Consider the area enclosed by the curves x = -2, x = 3, y = 3x2 - 70, and y = 12x + 26.

Q: What is the volume generated when the area bounded by y=2x2+1; x=1; x=2 is revolved about the line…

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Q: From the equation of x² + y² + z² = 25 and inside the equation x² + y² = 9 Calculate the volume of…

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Q: Find the area of the region enclosed between the curves y= 4 -x^2 and x=3 and x-axis within the…

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Q: How do you find the upper and lower limit of an integral volume equation?

A: To find :  The upper and lower limit of an integral to find the Volume of the given region.

Q: Determine the volume generated when the area bounded by the curves y-sinx and y=cosx from x=0 to…

A: Solution :-

Q: Find the area of the region bounded by the curve y= 1--x² and the x-axis.

A: Given equation of the curve: y=1-19x2 To find: Area of the region bounded by the curve and x-axis.

Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

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Q: Find the volume if the region bounded above x axis is rotated about the x axis

A: The volume for solid of revolution between curves is the volume of object between a curve fx and a…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)= 9x5 on the…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.