2.) Do what is asked. Answer must be in EXACT form only. Answers in numerical or decimal forms will be considered wrong. Make sure to draw the region R and write labels. A. A region R is bounded by the curve y = ln x, the x-axis, and the vertical line x = e2. If R is to be revolved about the x- axis, determine the volume of the solid generated.

Q: 1) Given the region bounded by the graphs of y = x sinx ,y = 0,x = 0, and x = T, find the volume of…

A: Volume of solid =>V=∫ab2πrh.dx

Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

A:

Q: Consider the region R bounded by the line y = 33 - 5x and the parabola y = 27 – x2. To find the…

A:

Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: 49. Consider the region R bounded by the graphs of y = f(x) > 0, x = a > 0, and x = b> a. If the…

A: Let the area of the region R be∫abfxdx.

Q: 1) Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

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

Q: Define as the region bounded by the functions u(y) = 2 and v(y) around the y-axis, what is the…

A: The region Q is bounded by the function u(y)=2 and vy=y24 between y=1 and y=2 The solid formed by…

Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: If the region R = {(x, y) | x > 1,0 < y < 1/x} is rotated about the x-axis, the volume of the…

A:

Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

Q: ind the volume of the solid generated by revolving the region bounded by the graphs of y = x + 5 and…

A:

Q: Consider the region R bounded by the graphs of y = ƒ(x) &gt; 0, x = a &gt; 0, and x = b &gt; a. If…

A:

Q: Given the region bounded by the graphs below, find the volume of the solid generated by revolving…

A:

Q: 49. Consider y = f(x) > 0, x = a > 0, and x = b > a. If the volume of the solid formed by revolving…

A:

Q: Suppose that R is the finite region bounded by y = x, y = x + 3, 0, and x 1. Find the exact value of…

A:

Q: Let R be the region bounded by the curve y = Vx, the line y = 1, and the y-axis a. Use the shell…

A: Given The equation of the curves is y=√x  ,  y =1  and   x = 0 .   Formula :- Shell method . V=2π∫ab…

Q: Let R be the region bounded by the graphs of y=x,x%39 and the x-axis, then the volume of the solid…

A:

Q: Suppose that RR is the finite region bounded by  y=x, y=x+4, x=0, and x=2. Find the exact value of…

A:

Q: 5. Use the method of Washers and Shells to find the volume of the solid generated when the region R…

A: Given, y=x2over [0,2] is revolved about the line y=-2.

Q: Let the region R be the area enclosed by y = 2x – 2 and x = Vy + 1. Find the volume of the solid…

A:

Q: The region bounded by y = Vr, y = 2, and the y-axis is revolved about the a-axis. Find the volume of…

A: The region is bounded by the curves: y=x ,     y=0    and   y axis

Q: a- Sketch the region bounded by the graphs x=0 , y=4 and y=Vx and find its area b- Find the volume…

A: (a)

Q: 3. If the region bounded by the curves y =x, y=0, and x =9 is the base of a solid, and cross…

A:

Q: 14 - Which of the following is the volume of the object that occurs when the region bound by the y=…

A: We sketch the region using a graphing calculator  The shaded region will rotate around the x axis

Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

A:

Q: he region bounded by y = e, y = 0, x = 0, and x = 1 is revolved about the y- xis. Find the volume of…

A:

Q: Let R be the region bounded by the graphs of y= /x, x= 9 and the x – axis, then the volume of the…

A:

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: Proceed as shown below

Q: Suppose that a region R has area A and lies above the x-axis. When R is rotated about the x-axis, it…

A: Use the disc method to find the W in terms of V, k and A.

Q: 2) ( ) Sketch and find the exact volume of the solid obtained by rotating the region B bounded by…

A:

Q: y = x² +9 %3D y= 18

A:

Q: A solid is constructed between the lines r = a, x = b, the graph of y = f(x) and the x-axis so that…

A: Given figure of solid with circular cross-section is ,

Q: 30. Find the volume obtained by rotating the region bound by the graph y = e"+e-2#, x = -2, = 3 and…

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

Q: 1. Consider the region bounded by y = x and y = √ x, shown below. x y Find the volume of the solid…

A:

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the curve y? = x?(a – x),…

A:

Q: Let M be the region in the first quadrant bounded above by the graph of y = 3x and below by the…

A:

Q: 2. Find the volume of the solid generated by revolving about the y-axis the area bounded by the…

A:

Q: 17. Find the volume of the solid that results when the region enclosed by y = √x, y = 0, and 2 = 9…

A: According to our guidelines, we can answer only the first problem or first three subparts of a…

Q: Let M be the region in the first quadrant bounded by the graphs of y=arctanx and y=(πx)/4. What is…

A: Given, y=tan-1xy=πx4 Revolving around x=2   To find: The volume of rotation of the bounded region.…

Q: Find the volume.

A:

Q: See the figure below and then consider the region R bounded by y=2√x, x-axis, and x=1. Show the…

A:

Q: 3. Find where the curves intersect, draw a sketch of the region, and compute the volume when the…

A:

Q: 1. Consider the region bounded by y = x and y = Vx, shown below. Find the volume of the solid…

A:

Q: (5) Find the volume and draw an illusration of the solid S obtained by rotating the region bounded…

A:

Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

A:

Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

A:

Q: 25. y = In x, x= 0, y = 0, y= 1

A:

Q: 2. Find where the curves intersect, draw a sketch of the region (label it completely), and compute…

A: Region is sketched. And volume is evaluated.

Q: 15. Find the volume by the parabole y² = of the solid generated by revolving y-axis, the area…

A:

Q: Let R be the region bounded by the graphs of y= /x , x = 9 and the x – axis, then the volume of the…

A: I use shell method to find volume about y axis