Find the exact value of the volume of the solid obtained by rotating the region bounded by y=5sqrt(x), x=0, and y=6, about the Y-axis.

Q: Find the volume of the solid obtained by revolving about the x-axis the region between y = 2x and…

A: Given curves:- y=2x and y=x2

Q: Find the volume of the solid generated when the region enclosed between y = cos x and y = 0for 0 ≤ x…

A: The volume of the solid generated when the region enclosed between y = cos x and y = 0 for 0 ≤ x ≤…

Q: Find the volume of the solid obtained when the region bounded by the x-axis, the y-axis, and the…

A: The given problem is to find the volume of the solid obtained when the region bounded by given…

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = Va, x…

A:

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = Vx, x…

A:

Q: Find the volume of the solid created by revolving the bounded region created by the graphs of y = Vx…

A:

Q: Compute the volume of the solid obtained by revolving the graph of y =1+x^2/2 on [0,1] about the…

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Q: Find the volume “V” obtained by revolutionizing the region between y=2√x  y  y=x around the x=-2…

A: To find volume obtained by revolutionizing the region between y=2x and y=x around x=-2. y=2xSquaring…

Q: Calculate the volume V of the solid obtained by rotating the region under y = x2 about the x-axis…

A: To find the volume V of the solid obtained by rotating under a region, use the formula, V=∫abπ(y)2dx…

Q: Find the volume of the solid obtained by revolving the region bounded by y = In x, y = -8, and x = 7…

A:

Q: Find the volume of the solid obtained by rotating about the x-axis, the region under the curve. y =…

A: Consider the curves, y=2x+3,y=0,  x=0    to  x=3 Consider the region:

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = VT, x…

A:

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = 3T, x…

A:

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x5,…

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

Q: Find the volume of the solid of revolution obtained by rotating the region bounded by the graphs of…

A:

Q: Find the volume of the solid formed when the region bound by y = e* + 3, x = 0, x = 3 and the x-axis…

A:

Q: Find the volume of the solid obtained by revolving the region { (x,y): 0 about the x-axis:

A: Integration of function expression with respect to variable x or y gives the area between function…

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by…

A: We have to find the volume of the solid obtained by rotating the region bounded by y=2sqrt(x) ,x=0…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 6x, x = 1, and y 0,…

A:

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

A:

Q: Find the volume of the solid formed by rotating the region enclosed by y = e + 2, y = 0, x = 0, x =…

A: Given regions are y=e4x+2,y=0,x=0,x=1.4.

Q: Find the volume of the solid obtained by rotating the region bounded by the curves y = x 2 – 3x + 2,…

A:

Q: Sketch the solid obtained by rotating the region underneath the graph of the function f(x)=x^(−4)…

A: We sketch the graph using a graphing calculator. The shaded region will rotate about the violet…

Q: Find the volume of the solid generated by revolving the region bounded by y = x² + 1, y = x + 3…

A: Given that,  y = x2 + 1y = x + 3 The Axis of rotation = X-axis In the Disk/Washer method strip is…

Q: Find the volume of the solid of revolution generated by rotating about x= -1, the region bounded by…

A:

Q: Find the volume of the solid obtained when the region under the curve y = x/4 – x2 from x = 0 to x =…

A: Given data:     The given expression is: y=x(4-x2)1⁄2. The given limits of x is: (a,b)=(0,2). The…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x² , 0, and a = 4, about…

A:

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 6 – a, y…

A:

Q: Find the volume of the solid generated when the plane region bounded by: y=e^(-x^2 )  and the…

A: The given problem is to find the volume of the solid generated when the given plane region in…

Q: Find the volume of the solid generated by revolving the region bounded by the curve y = In x, the…

A:

Q: Find the volume V of the solid obtained by rotating the region under the graph of f(x) = 1 over the…

A: The given curve is fx=1πx The interval is 1, 4 To find volume V rotated about the y-axis.

Q: Find the volume V of the solid formed by revolving the region bounded by the graphs of y= T – y = 0…

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Q: Find the volume of the solid whose base is the region bounded between the curves y = x and y = x²,…

A:

Q: Find the volume of the solid formed by rotating the region enclosed by y = e + 3, y = 0, x = 0, z =…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by 9x", x = 1, and y = 0, about…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y=x^4 and y=1 with 0 being…

A: We have given

Q: Find the volume of the solid generated when the region bounded by y = x2and y2 = x is revolved about…

A:

Q: find the volume of the solid obtained by revolving the region bounded by y = x - x2 and the x - axis…

A:

Q: y = Vx + 1 + x and the x-axis from x = 0 to x = 3 about the y-axis.

A: When rotating about y axis, we should use shell method to find the volume. The formula for volume is…

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = vT, T…

A:

Q: Find the exact volume of the solid whose region is bounded by y = 2 a + 2, y = 0, x = 3 and x =…

A: Given data : y=2x+2 , y=0x=3 , x=4

Q: Evaluate the volume of the solid obtained by rotating the region bounded by the parabolas x= Vy-1…

A: We have to find the volume of the solid obtained by rotating the region bounded by the…

Q: Calculate the volume of the infinite solid obtained by rotating the region under y = (x2 + 1) −2 for…

A: Use shell method and find the volume.

Q: Find the volume of the solid obtained by rotating the region bounded by the curves: y=x-1, y=D0,…

A:

Q: Calculate the volume of the solid produced by rotating the region enclosed by about x - 4x – 4y + 4…

A:

Q: Find the volume of the solid obtained by rotating the region bounded, by y x2 - 2x and y = x about…

A: The region bounded by the curves y=x2-2x and y=x about the line y=4 is as shown above.

Q: Find the volume of the solid obtained by rotating the region bounded by y 5x-x2 and y-x about the…

A:

Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y=6(x^2),…

A:

Q: 2. x = 4y – y² and x = 4 – y -

A: follow next step

Q: Find the volume of the solid generated by revolving the unbounded region lying between y = −ln x and…

A: Given that: y=-lnx   and   the   y-axis To sketch the region:

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.