x=y2 x=2-y2 What is the volume of the shape formed by rotating the region bounded by its curves around the x=-1 line?

Q: The region is formed by the graphs of y = 4Vx and y = 5 - x. Find the volume of the solid obtained…

A:

Q: 3. Find the volume of the solid generated by revolving about the line x 3 the region in y = 2x - 2…

A: To find : volume from the revolution.

Q: The area cut off by the x-axis and the curve y = x2-3x is rotated about the x-axis. Find the volume…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by the curves y=√2x, y=x^2/2,…

A: Given curves, y=2xy=x22 Using the washer method: Formula for the volume of the solid obtained by…

Q: Sketch the region bounded by the curves y = V-x² + 1 and y = 0 then find the volume of the solid…

A: The curves are y=-x2+1 and y=0

Q: A. Find the volume of the solid generated by revolving the region that is bounded y = x + 3 and the…

A: by Washer Method we know  Volume of a solid generated by revolving the region bounded by y=f(x)…

Q: 4x2 + 20x + 24, The region bounded by f(x) = x = 0, and y = 0 is rotated about the y-axis. Find the…

A:

Q: Find the volume V of the solid generated by revolving about the x-axis the region under the curve y…

A:

Q: 3. Find the volume of the solid form by the region bounded by the curves y = =,y = 2-x is revolved…

A:

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

A:

Q: A. Determine the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Find the volume of the resulting solid if the region under the curve y = 9/(x2 + 3x + 2) from x = 0…

A:

Q: 6. Find the volume of the solid formed by rotating the region enclosed by y=e2x+5, y=0, x=0, x=0.6…

A:

Q: Find the volume of the solid formed by revolving the region under the curve y = x² +1on the interval…

A:

Q: Q-3 calculate the Volume of the solid obtained by rotating the region bounded by the cerve y= 2X-X2…

A: We will draw a region first.  And volume of revolution can be obtained by Integration

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x - 3y - 2…

A: Given: y=√(x-2) , x-3y-2=0

Q: ermine the volume of the solid obtained by rotating the region bounded by y = √x and y = 3 and the…

A:

Q: a) Find the intersection point between curves 2=-2 and y=-/2x+2. Hence, find the area of the…

A:

Q: Use the washer method to determine the volume of the solid obtained by rotating the region bounded…

A: Given solid is the region bounded between y=10-6x+x2, y=10+6x-x2, x=1 & x=5. To find the volume…

Q: b) [. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x² +…

A: Solve the following

Q: Sketch the region bounded by the graphs of y = r2 and y = VI. Then find the volume of the solid…

A:

Q: Find the volume of the resulting solid if the region under the curve y 9/(x2 + 3x + 2) from = 0 to x…

A: I am solving only part a for the part b post the question again:

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

A:

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

A: (a) The equations are given as

Q: Estimate the volume of the solid by y= x- x' and x- axis that shown in figure below due to rotating…

A:

Q: The area of the region bounded by the x-axis and y=7x-x2 is revolved about the x-axis. The volume of…

A:

Q: Consider the infinite region in the first quadrant bounded by the graphs of y = 1 /x2 , y = 0, and x…

A: Given : The infinite region in the first quadrant bounded by the graphs of y = 1/x2 , y = 0, and x =…

Q: 1.

A:

Q: ind the volume generated by revolving the area enclosed by the curve x²+y²=25 about the line y-8=0.

A:

Q: The area bounded by the parabola y² + x - 2y = 1, the x — axis, and the line x = 2 revolves about…

A:

Q: Q3: Calculate the volume of the solid obtained by rotating the region bounded by the curve y = 2x -x…

A:

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

A:

Q: Sketch the region bounded by the graphs of y r and y = V. Then find the volume of the solid formed…

A:

Q: 1. y = 3x - x² and y = 3-x Find the volume of the solid generated by revolving about the line x = 4…

A:

Q: Q16 about the line y = -2 Find the volume of the solid obtained by rotating the region bounded by…

A:

Q: Q3(a). Find the volume of solid generated by revolving about y-axis the region bounded the 16 curve…

A:

Q: 2. Find the volume of the solid generated by revolving the region bounded by the parabola y = x…

A: I use washer method

Q: The region bounded by the curves y=x-x^2 and y=0 is rotated about t he y-axis. Find the volume of…

A: If a region is bounded by two curves y=f(x) and y=g(x) on an interval [a,b], where 0≤g(x)≤f(x), then…

Q: The region in the first quadrant bounded by the graph of y sec x, x=, and the axes is rotated 4…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the parabola y = x² and…

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: Sketch the region bounded by the graphs of y =x2 and y = x1/2 . Then find the volume of the solid…

A:

Q: The region bounded by the curve: y = e * and y=0 for x20is rotated about the x – axis. Calculate its…

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

Q: The region bounded by f(r) -2+10x + 48, x-0, and y=0is rotated about the y-axis. Find the volume of…

A:

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: The region in the first quadrant bounded by Y = -3x + 6, the x-axis and the Y-axis is rotated around…

A:

Q: d the volume of the solid formed by revo

A: Given : The equation of the parabola y2 = 9x and the line y = 3x , about y - axis.

Q: a) Find the points of intersection of the curves y = -3x? and y = 2x2 - 80. b) Find the Volume of…

A:

Q: Q3) Find the volume of the solid generated by revolving region bounded by the curve (y-e*) & the…

A: Integral

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.