Find the volume of the resulting solid if the region under the curve y = 4/(x2 + 5x + 6) from x = 0 to x = 1 is rotated about the x-axis and the y-axis. (a) the x-axis     (b) the y-axis

Q: Find the area of the region bounded by the graph of f(x) = 2.x3 – 36x2 + 192x + 5 and the x-axis…

A: f'(x) = 6x2 -72x +192 (x-8)(x-4) =0

Q: The region bounded by y = x² – 3x + 2 and y = 0 is rotated about the y-axis. Find the volume of the…

A: The given curves are,

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: We will find the volume of the solid as following.

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

A: The volume for solid of revolution between the curves y=3x4 and y=0 around the x-axis on interval…

Q: Find the volume of the solid obtained by rotating the region bounded by the curves x2 −y2 =9 and x=5…

A: Consider the provided question, The graph of the given curve is drawn as, The required volume of…

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 obtained by revolving the region in the first quadrant bounded by the 2…

A: Consider the given curves and plot them. Mention the intersection points for the 2 curves. The…

Q: Find the volume generated by revolving the first quadrant area bounded by the parabola y2=8x and its…

A: We have to find the volume generated by revolving the first quadrant area bounded by the parabola…

Q: 4. The region bounded by the curve y = x² + 1 and the line y = -x + 3 is revolved about the x-axis…

A: We have to find the volume of solid.

Q: Find the volume of the Solid generated by revolving the region bounded by y = -2x? and y = x2 - 3 ,…

A: According to the given information it is required to find the volume of the solid generated by…

Q: Find the volume of solid generated by revolving the region bounded by the curves and lines about the…

A:

Q: Find the volume of the region bounded by y=x^2 Below the x axis And on the right by the line x=3…

A:

Q: Find the volume generated when the area bounded by the two curves of x2 = 4y and y2 = 4x is revolved…

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: The region bounded by y = x² + x – 2 and y = 0 is rotated about the x-axis. Find the volume of the…

A: Given query is to find volume of the solid generated.

Q: alculate the volume of the solid obtained by rotating the region bounded by the function y = x^2,…

A: given function is y=x2the line y=-2 from x=0 to x=2find the volume V=∫abπfx2-gx2dx

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

A: The given curves are: y=-csc-1x        and       y=-π2    from x=1  to  x=2

Q: Find the volume of the solid formed when the region bounded by the graph of​ f, the​ x-axis, and the…

A: Given: f(x)=x0≤x≤12x-41<x≤4-2x+154<x≤5Formula: Volume =π…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We have to draw the region enclosed by the given curves and the solid generated by the revolution of…

Q: Find the volume of the solid formed by rotating the region enclosed by y = ln ( x − 3 ) , y = 0 , x…

A:

Q: Find the volume of the solid of revolution formed by rotating the area under y=9-x2 over [0, 3]…

A: Given:  f(x)=y=9-x2 limits of x are (0,3) The expression for the volume is given , we will integrate…

Q: A solid is formed by revolving the region bounded by the graph of f(x)= x^-p and the x-axis fro 0<x≤…

A: A solid is formed by revolving the region bounded by the graph of f(x) = x−p and the x axis for 0…

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

A:

Q: Find the exact value of the volume of the solid formed by revolving the region bounded b the graph…

A:

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

A: Given:

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

A: Given:

Q: The region bounded by X = 1 – y and X = 0 is rotated about the line X = 2. Find the volume of the…

A: To calculate the volume bounded by the given curves

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

A: Plot the curves and find the region enclosed by the curves. The shaded region is the region enclosed…

Q: Find the volume of the solid generated by revolving the region bounded by the curve x2 y2 = 16 and…

A:

Q: 1. Find the area of the region bounded from the right by the curve x = 4- y2, from the left by the…

A:

Q: Determine the volume of the solid generated by revolving the region between curves about the line x…

A:

Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x)=64-4x^2…

A: Given query is to find the volume of the solid generated.

Q: 12. The area between curve y = x(4 – x)² and the x-axis is rotated through 360° about the x-axis.…

A: First draw plot of the curve on xy plane.

Q: find the volume of the revolution of the area bounded by y=4x-x^2 and y=3 rotated about the y axis.

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 that results when the region in the first quadrant bounded by the curve…

A: Find the volume of the solid that results when the region in the first quadrant bounded by the curve…

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

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

Q: Use the cylindrical shells to find the volume of the solid obtained by rotating the region bounded…

A: Since you have asked multiple questions, we have answered the first question. If you want the second…

Q: Determine the volume of the solid generated when the region bounded by the curve y² = x³, x = 2 and…

A: The volume of revolution of the area bounded by the curve y=f(x) about the x-axis between the limits…

Q: problem in photo attached

A: The given curves are x = 1­– y4 and x = 0.Compute the region bounded by the given curves as follows.

Q: The region bounded by y = x – 3x +2 and y = 0 is rotated about the y-axis. Find the volume of the…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = x3 , x =…

A: Here, the given region is bounded by the graphs of y=x3, x=2 &amp; y=0 is shown:

Q: Find the volume generated by revolving the area bounded by the parabola y2=8x and its latus rectum…

A: We have to find  the volume generated by revolving the area bounded by the parabola y2=8x and its…

Q: Find the volume generated by rotating the region in the first quadrant bounded by y=exy=ex and the…

A: Consider the equation for x∈0, ln 3: y=ex……1

Q: 4. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

A:

Q: solid is formed by revolving the region bounded by the graphs of y=5x, y=1/5ln(1/4),y=7, and the…

A:

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

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

Q: Find the volume of the solid obtained by rotating the region under the graph of the function…

A: Given      fx =2x+1,    0,1       Volume  V=∫abπ fx2-gx2 dx

Q: Compute the volume of the solid formed by rotating the region pounded by = 1 - x² and y = 0 about…

A: Given:- y = 1-x2 and y=0 To find:- Volume about x axis of solid formed by given curves and line

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.