The region bounded by the positive x axis , the positive y axis, and the curve y = √a^2 - x^2 is revolved about the y- axis. Find the volume of solid generated

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: Find the volume of the solid obtained by revolving the region bounded by the graph of f (x) = 2/x…

A: Please refer the attached image for complete solution.

Q: The region bounded by y=√(5-x), x=1, and y=0 is revolved around the (a) x-axis and the (b) y-axis.…

A:

Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: Find the volume of solid generated when area bounded

A: Given: The area bounded by  y=x2 and y=x is revolve about x=2.

Q: Find the Volume: Rotate the region bounded by y = 7 - x², x = -2 and x = 2 and the x-axis about the…

A: Volume of the solid of Revolution :  Suppose y=f(x) is a continuous non-negative function on the…

Q: Find the volume generated by rotating about the x-axis the region bounded by the 1 graphs of the set…

A: Volume is the measure of the amount of space occupied by a closed surface. The equation for the…

Q: Find the volume of the resulting solid of revolution located in the first quadrant bounded by the…

A: According to question, Given curve, y=6x-x2

Q: The region bounded by the graph of y = and the x-axis on the interval [0,12] is revolved about the…

A: detailed solution is given below

Q: The area bounded by the y-axis, the line y = 1 and that arc of y = sinx between x = 0 and x = 1/2 is…

A: The given region is: y-axis,   y=1,  and the arc  y=sin x      between   x=0  to  x=π2

Q: A region bounded by the parabola y = 4x - x2 and the x-axis is revolved about the x-axis. A second…

A: A region bounded by the parabola y=4x-x2 and the x-axis is revolved about the x-axis.A second region…

Q: Find the volume of the solid generated by rotating the region bounded by f(x) = 2-x², g(x)=√1-x², x…

A: We know The volume of the solid formed by revolving the region between curve fx and curve gx around…

Q: Determine the volume of the solid formed by rotation about the y-axis of the region bounded by 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: SOLVE FOR THE VOLUME GENERATED BY SOLIDS OF REVOLUTION USING INTEGRATION. USING WASHER METHOD Find…

A:

Q: Find the volume of The region R bounded by the graph of y=4sinx and the​ x-axis on [0, π] is…

A:

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

A: Given: y=x-2 , y=ex-3 , x=2 . Therefore, x-2=ex-3⇒x=3. Now, put x=3 in y,we get : y=3-2=1.…

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

A:

Q: The area bounded by the curve y^2 - 4x and the line 2x - y= 12 is revolved about the y-axis. Find…

A:

Q: The region in the first quadrant that is bounded above by the curve y = ex - 1, below by the x-axis,…

A: Express the integral as below.

Q: The region bounded by the curve y =x and the x-axis between x=0 and x = 1 is revolved around the…

A: It is given that, the curve y=x2 and the axis between x-0, x=1 is revolved aroud the line y=1We have…

Q: The area bounded by the curve y^2 = 4x and the line 2x - y 12 is revol %3D about the y-axis. Find…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of y = 2x² + 1…

A:

Q: Find the volume of the solid formed by rotating the area between the square with a side length of 2…

A:

Q: find the volume of the solid generated by revolving each region about the given axis. The region in…

A: Given curve second quadranty=-x3below by x axisleft by the line x = -1about line x = -2

Q: Find the exact value of the volume of the solid that results when the region bounded by the given…

A:

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

A: find intersection

Q: The region bounded by the parabola y = x and the line y = 2x is revolved about the line y = -1. Find…

A:

Q: A 6-inch-tall plastic cup is shaped like a surface obtained by rotating a line segment in the first…

A: Given: A 6-inch-tall plastic cup is shaped like a surface obtained by rotating a line segment in the…

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: Find the volume generated by revolving about the line x – 4 = 0 the area bounded by the curve x2 =…

A: Given : x²=8y and line y-2=0 Revolving about x=4

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: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

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

A:

Q: The region bounded by the curve y = x and the line y = 3x, is revolved about the line x=-3. Find its…

A: Given functions are                                                         y=x2y=3xx=-3 points of…

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

A: Solution-Lets draw the curve and the lines and identify the bounded area.

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 y = 2x + 1…

A:

Q: The area bounded by the curve y=(x^2-2)^2 and the x-axis is revolved about the y-axis. Find the…

A: the volume revolved about x-axis given by the curve f(x) and limits a to b is  volume = π∫ab(fx]2dx

Q: Find the volume of region revolving about y axis, and bounded by x-axis and y = 5Vx,0 < y < 5

A:

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

A:

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: 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: Find the volume generated by revolving about the y-axis in the first quadrant bounded by y^2-3x+3=0…

A: We have, y2-3x+3=0⇒x=y2+33 x-4=0   Volume generated by revolving the bounded region can be…

Q: Find the volume of the solid generated by revolving the region about the given line. 14) The region…

A:

Q: . The area bounded by the curve y = 3 – 2x + x² and the line y = 3 is revolved about the line x = 5.…

A: The volume of the solid of the revolution can be calculated using the shell method. The formula to…

Q: Find the volume if the region bounded above x axis is rotated about the x axis

A: The volume for solid of revolution between curves is the volume of object between a curve fx and a…

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

A:

Q: y²- 4y + 2x = 0, x = 2 and x-axis

A:

Q: Find the volume of the region bounded above by the planez = 2 - x - y and below by the square R: 0 ≤…

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.