The base of a solid is the region bounded by the line y = 9 and the parabola y = x². Cuts perpendicular to the xy-plane and parallel to the y-axis are isosceles right triangles, where all the right angles are on the line y = 9. Please determine the volume of this solid.

Q: Find the volume of the solid that results when the region bounded by x = y and x = y + 12 is…

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Q: The base of a solid is the region in the first quadrant bounded by the graph of y =1- and the z- and…

A: Since each cross-section is perpendicular to the x-axis is a square, we have to find the area in…

Q: find the volume of the solid obtained by rotating the region enclosed by the graphs aboutthe given…

A: We graph the region using a graphing calculator.  The shaded region is rotating about the x=-2 axis…

Q: The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is re- volved…

A: Please refer the attached image for complete solution.

Q: 42. y = x², y= 12 – x, x = 0, about y : 0, about y = 15 || -

A: We have to sketch the region first.

Q: Find the volume formed by revolving about the line y = 2a, the area bounded by that line, the curve…

A: As per rule of Barbtleby we can solve only one question at a time and we can solve only three…

Q: Find the volume of the solid whose base is given by 9. whose cross-sections perpendicular to the…

A: We will first find the area of cross section. Then integration of Area will be required volume of…

Q: Find the volume of the solid generated when the region enclosed by y = \2x + 8, y = x, x = 0 is…

A: If y=f(x) is a function, then the independent variable x is called the input of the function, and…

Q: what is the volume generated if the area bounded by the cirves x2 =8y , x=4 and y= 0 is resolved…

A:

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x), y = 0, and x = 49 is…

A:

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 16 and whose cross…

A:

Q: Find the volume of the solid formed by rotating the region enclosed by eA# + 5, y = 0, x = 0, x =…

A: olume by shell method is given below

Q: Find the volume when the region bounded by y = 2x², x = 0, x = 4, and y = 0 is revolved about the…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Find the volume of the solid whose base is the semicircle y = /25 – x² where –5 < x < 5 and the…

A: Given the base of the solidy=25-x2 , y&gt;0The intersection of the base with the x-axis :Put y =…

Q: ) Find the volume of the solid whose base is the region in the first quadrant bounded by y = x5, y =…

A: Here, the cross-sections perpendicular to the x-axis are semicircles whose base span from y=x5 &amp;…

Q: If the region enclosed by the y-axis, the line y=2 and the curve y=sqrtx is revolved about the…

A: Proceed as shown below...

Q: Find the exact value of a volume of the solid obtained by rotating the region bounded by y=5square…

A:

Q: What is the exact volume of a solid that is formed by rotating the region bounded by g (x) = †x² +1,…

A:

Q: Find the volume formed by rotating the region enclosed by: 6.2y and y° = x with y > 0 about the…

A:

Q: What is the exact volume of a solid that is formed by rotating the region bounded by g (x) = †x²+1,…

A:

Q: Find the volume of the solid generated by revolving about the line x = 2, the area bounded by y =…

A: The equation of the curves are  C1: y = x2C2: x= 2C3: y = 0 The axis of the revolution is x = 2 To…

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y 1, and the…

A: Here, to find the volume of the solid whose base is the region in the first quadrant bounded by…

Q: The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

A: Please find the answer.

Q: The region enclosed by the graph of the lines; y = lnx, y = 0,x = 0 and y = 1 is revolved about the…

A: The region is y=lnx, y=0 and x=0 and y=1 It is revolved about x=axis,  To find the volume of the…

Q: Find the volume of the solid formed by invoving the region by the graphs y=x^3 , y = 0 , x = 1 ,…

A: Answer

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle whose…

A:

Q: Find the volume of the solid generated when the region enclosed by y = Vx + 2, Y = /5x, and y = 0 is…

A:

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 9 and whose cross…

A: To find the volume of the solid whose base is bounded by the given circle and whose cross-sections…

Q: Find the volume formed by rotating the region enclosed by: x = 7.8y and y = x with y > 0 about the…

A:

Q: Find the volume of the solid whose base is the region |x|+|y|≤4 and whose vertical cross sections…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: . Find the volume of the solid whose base is the region bounded by the semicircle y = 1– x² and the…

A:

Q: find the volume,The region bounded in back by the plane x = 0, on the front and sides by the…

A: Given

Q: The region bounded by the curve y = x2 + 1 and the line y = −x + 3 is revolved about the x-axis to…

A:

Q: find the volume of the solid obtained by rotating the region enclosed by the graphs aboutthe y-axis…

A:

Q: Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y =…

A: According to the Q&amp;A guideline, only the first question can be solved. Please repost rest…

Q: A solid is formed by revolving the region bounded by the graphs of y = 5x, y = In (r), y = 7, and…

A:

Q: The base of a solid is the region in the first quadrant bounded by the curve y = Vsinx for 0SxST. If…

A:

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane y + z…

A: Given that the region in the first octant bounded by the coordinate planes, the plane y+z=2 and the…

Q: Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y =…

A:

Q: Find the volume of the solid whose base is bounded by the given function with the indicated cross…

A: To calculate the volume you have to rotate the function along the line ,x=0 which is perpendicular…

Q: Find the volume of the solid whose base is the region |x| + |y| ≤ 1 and whose vertical cross…

A:

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(2x + 8), y = x, x = 0 is…

A: Given :     To find the volume of the solid.

Q: find the volume of the solid that results when the region enclosed by the curves x=y2 and x=y+2 are…

A: Given curves are x=y2 and x=y+2          (1) f(y)=y2 and g(y)=y+2 From (1)…

Q: Find the volume formed by rotating the region enclosed by:   x=8y  and  y^3=x  with  y≥0   about…

A:

Q: A solid is formed by revolving the region bounded by the graphs of y = 5x, y = In (x), y = 7, and…

A:

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x + y…

A:

Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

A: If is a function, then the independent variable x is called the input of the function and the…

Q: Find the volume of the solid formed by invoving the region by the graphs y=x^3 , x = 1 , about x = 2

A: We first sketch the region using a graphing calculator.

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.