Find the volume of the solid that results when the region enclosed by the given curves is revolved about the x-axis. 1. Y= 1+x^3 , x=1 , Y=9.

Q: y2- 4y + 2x = 0, x = 2 and x-axis

A:

Q: The region between the curve y = 2/x and the x-axis from x = 1to x = 4 is revolved about the x-axis…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the x…

Q: The region in the first quadrant that is bounded above by the curve y= 1/x, on the left by the line…

A:

Q: 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x…

A:

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: 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 red curve is y=10-x^2 The black curve is…

Q: xy = 4, y = x,y = 1; about the x-axis.

A: Find your answer below

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y =2x + 1…

A: For the point of intersection of the curves, we will solve the given two curves as:…

Q: Find the volume of the solid formed by rotating the region bounded by y = e^(2x) and y = 2Vx from x…

A:

Q: Geometry problems Use a table of integrals to solve the following problems.

A: Given Data The equation of the region is y=1x+4. The interval on x-axis is [0,12].   Arrange the…

Q: Find the volume of revolution of the region bounded by the curves x = (y-2)½, y = x + 4, and y-axis…

A: Plot the graphs:

Q: 4. Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2…

A:

Q: The region in the first quadrant that is bounded above by the curve y = 1/(x^1/2), on the left by the…

A: Given that the function  y = 1x, x = 14 , y =1

Q: Determine the volume of the solid obtained by rotating the region bounded by y = cosh x , y-axis, x…

A: Use the shell method to solve for the volume. Draw the graph for the functions given.

Q: Find the volume of the solid of revolution generated by revolving the region in the first quadrant…

A:

Q: 2. Sketch the graph and shade the region enclosed by the curves y = x² and x axis from x=0 x=2. Find…

A: Given region enclosed by - y = x2 x =0 x =2

Q: The region bounded by the curve y = x², axis, and the line x = 2 is revolved about the y-axis. What…

A:

Q: Find the volume of the colld_generated by. revolving the area bounded by the given curves_ about the…

A: We need to find volume.

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

A:

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

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: 5. Find the volume of the solid generated by revolving about y axis, the area bounded the y=(x²-4)²…

A:

Q: Find the volume of the solid whose base is in the first and second quadrants bounded by y=16−4x2 and…

A:

Q: To find the volume of the solid generated by revolving the area bounded by the given curve about the…

A: The volume of the solid generated by revolving the area bounded by the curves f(x) and g(x) over the…

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 whose base is bounded by the given function with the indicated cross…

A: 1. Given: x2+y2=4, quarter-circlesx=±2 are the limitsy=4-x2volume =π∫aby2dx

Q: Find the volume of the solid of revolution generated by revolving about the​ x-axis the region under…

A: Given: y=10x from x=10 to x=19 To find: The volume of the solid of revolution generated by revolving…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x and y =…

A: Given: y = x,  y = x2  To find: Volume of the solid formed by revolving the region bounded by the…

Q: y = x y = 12 – x, x = 0, about y -2 x > 0

A: Given that: y=x2,  y=12-x  ,  x=0,  about  y=-2,x≥0 The volume of the solid between the curves…

Q: The region in the first quadrant that is bounded above by the curve y = 1/(x^1/4) , on the left by…

A: Solution Given The region in the first quadrant that is bounded above by the curve y = 1/(x^1/4) , on…

Q: y = x² – 3x; y + x = 0 about the x-axis

A:

Q: A region in the first quadrant is bounded above by the curve y = cosh x, below by the curve y = sinh…

A: A region in the first quadrant is bounded above by the curve y = cosh x, below by the curve y = sinh…

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

A:

Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 7y and y^3= x with y…

A:

Q: Find the volume of the solid formed by revolving the region bounded by the graph of the equation…

A: ⇒The volume of the solid formed by revolving the region bounded by the curve  y = f (x)        and…

Q: The region between the graph of y = sinx and the x-axis on the interval [0, #] is revolved about the…

A: use the cylindrical shell method for finding the volume of solid

Q: Find the volume of the solid that results when the region enclosed by 1 x² and x = 6y² is revolved…

A:

Q: 4. Compute for the volume of the solid formed by rotating the shaded area about the x- axis. * 30-…

A: Given: f(x)=25-x2

Q: 23. The region bounded by the curve 4y = x, the line x = 4 and the line y = 1, is rotated through…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A: The volume of the solid rotating a curve about y-axis is given by the formula, V=∫cd πx2 dy  where c…

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 that results when the region enclosed by the given curves is revolved…

A:

Q: Find the volume generated by rotating the region in the first quadrant bounded by y=e^x and the…

A: Answer

Q: Find the volume of the solid generated by revolving the region bounded by the y = x?and y = 6x– 2x2…

A:

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

A: Given: The curve y=x2+1 and the line y=-x+3

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

A: Given that : The region bounded by the curve y = x2 + 1 and the line y = 3 − x is revolved about the…

Q: y²- 4y + 2x = 0, x = 2 and x-axis

A:

Q: 6. Find the volume of the solid generated when the area of the region between the curves y = Vsinx,…

A:

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.