The region bounded by the y-axis, f(x) = 8 – x² and g(x) perpendicular to the x-axis are semicircles. Find the volume of this solid. = e forms the base of a solid. Cross sections

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

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Q: The region enclosed by the curve y = sech x, the x-axis, and the lines x = +- ln sqrt(3) is revolved…

A: Given:

Q: The region bounded by the graphs of y=x^2 and y=6-|x| is revolves around the y-axis. What is the…

A: solution is given below

Q: The base of a solid is the region in the first quadrant bounded by the graph of y =1- and the z- and…

A: Since each cross-section is perpendicular to the x-axis is a square, we have to find the area in…

Q: 9. Find the volume of the solid whose base is the region enclosed by y = 2 –- x² and the x-axis and…

A:

Q: The square region with vertices (0, 2), (2, 0), (4, 2), and (2, 4) is revolved about the x-axis to…

A: Find the side, perimeter and area of square.

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: The solid lies between planes perpendicular to the x - axis at x = 0 and x = 4. The cross - sections…

A: The diagonal of square is between the parabolas, The solid lines are in between the interval,

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: The region in the first quadrant that is enclosed by the x-axis, the curve y = 5/(xsqrt(5 - x)), and…

A:

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

A: To find the volume of the solid generated be revolving the region bounded by the graphs of y=2x2+1…

Q: The base of a solid is the region between the line y = 4 and the parabola y = x'. The cross sections…

A: The base of the solid is the region between the line y=4 and y=x2. The cross sections are the…

Q: The base of a solid is bounded by y=2-x, y=-2+x, and.x=0. Find the volume of the solid if its cross-…

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

A:

Q: The area bounded by the parabola ay = x², %3D the x-axis, and the line x = b is revolved about the…

A:

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: The region bounded by the curve y x2 + 1 and the line the x-axis to generate a solid. Find the…

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Q: Evaluate the volume of the solid generated by revolving the plane region about an axis. Show the…

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

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

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

A: Please find the answer.

Q: Consider the solid whose base is bounded by the x-axis and the curve y = f(x) = 9-x on the interval…

A: Here b=h

Q: Calculate the eight approximation to the volume of a solid obtained by rotating the graph around the…

A: The given function is y=cosx and the interval is 0,π6. Recall the fact that the volume of the solid…

Q: The base of a solid is the region in the first quadrant between the graph of y = x and the x-axis…

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Q: The base of a solid is the region in the first quadrant bounded by the graph of y=2x-x^2 and the…

A: *to find:- Volume of solid.

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: Calculate the volume V obtained by rotating the region enclosed by the graphs y = x, x = 8, and the…

A:

Q: 3. Find the volume of the solid generated by rotating the region bounded by the graph of y = 2x – x2…

A: Given: y=2x-x2 and x axis about  y -axis

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

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Q: 3. The base of a solid is a region bounded by the lines y = 2x−2 and y=−x+4 and the x- axis. If…

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Q: Find the volume of the solid generated by revolving the area of circle: (x-2)²+y²=4; about the x…

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:

Q: A solid lies between planes perpendicular to the x-axis at x = -1 and x = 1. The cross-sections…

A: given that y=-1-x2 and y=1-x2x=-1,x=1find the volume of the solid

Q: The region bounded by the graph of y=2r-x and the x-axis is the base of a solid. For this solid,…

A:

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

A: Given: The following graph is drawn for the both equations.

Q: The region bounded by the graph of y=Vx+2, the x-axis and the y-axis rotates about the x-axis. Find…

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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: Find the volume of the solid obtained by rotating the region between the curves y = 3x - x³ and…

A:

Q: Find the volume generated by revolving the region under the graph about the y axi

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

A:

Q: The region between the curve y = 1/x2 and the x-axis from x = 1/2 to x = 2 is revolved about the…

A: Graph the given situation, shaded region is being rotated about y axis

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: The region bounded by the curve y = √x, the x-axis, and the line x = 4 is revolved about the x-axis…

A: y=x⇒x=y2&x=4. Now when x=0, y=0=0. & when x=4, y=4=2.

Q: Please show steps.

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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: Find the volume of the solid whose base is the region x+ y < 3 and whose vertical cross sections…

A:

Q: Find the volume of the solid bounded above by the graph of x2 + y2 +z2 = 5 and below by the graph of…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: The region in the first quadrant that is enclosed by the x-axis and the curve y = 3x√(1 - x) is…

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.