16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis by three units over the interval 1 < x < 3 to generate a solid. Solve to find the surface area of the obtained solid then determine the length of this curve?

Q: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

A:

Q: 1. Let a be a positive number. Find the surface area of the solid obtained by revolving the curve…

A: We use the disk method to find the volume

Q: Find the area of the surface generated by e + e -y revolving the curve x = 2 0sys In 6 about the…

A: To find the surface area generated by revolving the curve x=ey+e-y2,0≤y≤ln6 about the x-axis. We…

Q: b) consider the area between the X-aXis and the curve y= Sin2x for Os X<#/2. when this area is…

A: Let's find.

Q: 5. Find the area of the surface obtained by rotating the curve about the x-axis: x' + 6. 1 <x<1 1 2x

A:

Q: ind the volume of the resulting solid if the region under the curve  y = 8/(x2 + 3x + 2)  from x =…

A: Consider the curves y = 8x2+3x+2, x=0, x=1 about x-axis For this region of the disk is y = 8x2+3x+2…

Q: Compute the surface area of revolution of y=sinxy=sin⁡x about the x-axis over the interval [0,7π]

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Q: 12. Find the surface area for the surface of revolution formed by revolving the curve y = v4 – x?…

A:

Q: 15. a) Sketch the region enclosed by the linex = 3 and y = 1 and the curve xy = 9, %3D and find its…

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Q: 7. (a) Sketch the area R enclosed by the given the curves y =-r',y -1= 2 and z = 0. (b) Set up, but…

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Q: S be the region in the first quadrant bounded by the graphs of y = = and y = x, as shown in the…

A: In this question, the concept of volume of the revolution of solid is applied. Integration can be…

Q: (b) Set up a definite integral that is equal t length of the portion of the parabola y which serves…

A: Introduction: The washer method is used to calculate the volume enclosed by two functions. In this…

Q: The region between the curve y = Vxe- and the x-axis for0 <r<∞ is rotated about the r-axis to create…

A:

Q: 8) Consider the curve y ³ = 3x from (0, 0) to (8/3, 2). What integral finds the surface area of the…

A: Given,            The curve y3 = 3x from 0, 0 to 83, 2.

Q: 2. The arc of the parabola y = x² from (1, 1) to (2, 4) is rotated about the y-axis. Find the area…

A:

Q: 2. a) Sketch the region enclosed by the curves y=-x² +3x and y= x². Hence, find the area of the…

A: We have give curves y=-x2+3x and y=x2its graph is  Now find point of intersection of curves…

Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A:

Q: 4) Evaluate , z dV using rectangular coordinates, where Q is the solid in the first octant bounded…

A: In the first octant,  x≥0y≥0z≥0    Thus x, y and z cannot be less than 0

Q: 7. Find the volume of the solid generated by revolving the region bounded by the curves 3πT y=4 y =…

A:

Q: 3. Find the surface area generated by revolving the curve y = 2+ cos 0, x = sin 0 ; 0 <O< 2n about…

A:

Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

A:

Q: 3. Find the surface area generated by rotating y=- bounded by y=0_ x=0 , and x=9 about the the…

A: Surface area generated by rotating a curve y = f(x) about the x-axis from x = a to x = b is given by…

Q: 2.) Find the exact area of the surface obtained by rotating the curve about the x-axis y= cos(÷x) 0…

A:

Q: Find the surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: Find the area of the surface generated by e +e -y eY + e -y in the X= revolving the curve x= -In 3…

A:

Q: b) Find the surface area of the region under the curve 2/3 2/3 =1 by revolving about x-axis. a

A: b We have to find the surface area of the the region under the curve xa23+ya23=1by revolving about…

Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

A:

Q: 3 2. The solid whose base is the region bounded by the curve y= /cos(x) and the x-axis on and whose…

A: (2) To find: The volume of bounded region by slice method.

Q: Find the surface area of revolution about the x-axis of 6x +1 over the interval 2 < z < 3

A: Given y=6x+1 over the interval 2≤x≤3

Q: 42) Find the surface area of the solid that results when the region in the first quadrant bounded by…

A:

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

A:

Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: у 3 1 + sin х, 0 <x< т/2 y

A: The given curve is y=1+sinx and the limit is 0≤x≤π2 The Surface area is given by S=∫x2πy1+y'2dx or…

Q: Find the surface area of the solid that results when the region in the first quadrant bounded by the…

A:

Q: Л Define R as the region that is bounded by the graph of the function f(x) = -3√3 sin (x), the…

A: To find the volume of the solid that is obtained by revolving the region bounded by below curves…

Q: :-1, 8. Find the volume of the solid obtained by rotating the region bounded by the curves y = y =…

A:

Q: 2. Find the area of the surface obtained by revolving the curve g(x) = Vx +1 on the interval 0 < x <…

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Q: Express the area of the surface obtained by rotating the curve y =In sec(2x) between x = 0 and x =…

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Q: 8. Calculate the area of the region within the ellipse x2/a² + y²/b² = 1 parameterized by x = a cos…

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

Q: 15 Find the area of the surface generated by revolving x = 4/4- y,0sys about the y-axis. x=4/4-y Set…

A: find the area of the surface  generated by revolvigx=44-y, 0≤y≤154about y-axis

Q: 5. The external fuel tank for a space shuttle has a shape that may be obtained by revolving the…

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: 3. Find the volume of the solid under the plane 3x+ 2y – z = 0 over the shaded region between the…

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Q: The area in the first quadrant, bounded by the curve y = 2x1/2, the y-axis and the line y – 6 = 0 is…

A:

Q: ху — 4, 1 <x< 8

A: Surface area.

Q: 9. Find the area of the surface obtained by rotating the curve y = x',0sxs2 about the x-axis.

A: Given : y = x³, 0≤x≤2 about the x-axis

Q: Find the surface area of the solid that results when the region in the first quadrant bounded by the…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x.

A: Given: y=e-9x and 0, 1 To find the surface of revolution about the x-axis on 0, 1 The formula for…

Q: The volume of the solid generated by the curve y = e¯ª, between x = 2 and x = 7 about the x – axis…

A: Given curve, y=e-x x=2  and   x=7

Q: 9:(a): Find the area bounded by the curve y = = -x, the line y = x, and the line y= 2. (b) : Find…

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Q: Find the surface area of revolution about the x-axis of y = 6 sin(7x) over the interval 0 < x < 7

A: Here we have y=6sin(7x)  We have to find surface area of revolution about x axis in interval 0 to…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.