Find the area bounded by the function below and the x-axis and the volume generated if area is revolved about the x-axis. Compare the volume if the area is revolved about the y-axis. (X if 0 < x<1 f(x) 1 2 -x if 1

Q: Let f (x) = |x³ + 64| Find the area A of the region between the graph of f and the x axis on the…

A: here we have ............the x-axis .............the given function  .............the given interval…

Q: Let the region R be the area enclosed by the function f(x) = 2e" and g(x) = 7x + 2.Find the volume…

A:

Q: Let the region R be the area enclosed by the function f(x) = x° + 2 and g(x) = 4x + 2. If the region…

A: Given - Let the region R be the area enclosed by the function f(x)=x3+2 and g(x)=4x+2 To find the…

Q: Consider the function g (x) = †x +1. What is the exact volume of a solid that is formed with a…

A: Consider the given function whose volume is required to calculate. The volume for solid of…

Q: A football is 10.8 inches from tip to tip and 7 inches in diameter at its thickest. The shape of the…

A: Consider f(x)=-0.12x2+35. f(x)=0⇒-0.12x2+3.5=0⇒x2=-3.5-0.12⇒x=3.50.12 ≈±5.4 We find the volume by…

Q: Let the region R be the area enclosed by the function f (x) = ln (x) – 2 and g(x) = ;x – 3.Find the…

A: Given functions are fx=lnx-2 and gx=12x-3 about the line y=1. Formula used: Washer method:…

Q: Approximate the area under the graph of f(x) and above the x-axis using n rectangles. f(x)=25-x2…

A: f(x)=25 - x2 from a=-5 to b=5; n=2; use midpoints.  Width = Δx = (b - a) / n = (5 - (-5)) / 2 = 5

Q: Let the region R be the area enclosed by the function f (x) = e®, the horizontal line y = 4, and the…

A: Given that , fx=ex And  y=4. If the region R is the base of a solid such that each cross section…

Q: Let the region R be the area enclosed by the function f () = e² – 1 and g(x) = 4x. If the region R…

A:

Q: Approximate the area under the graph of f(x) and above the x axis using n rectangles

A: Given function is: fx=4x Number of rectangles is n=4. Limit of x is, a=2 b=6

Q: Let the region R be the area enclosed by the function f (x) = ² +1 and g(x) = 2x + 1. If the region…

A: The objective is to find the volume of the solid. Region R is the area enclosed by the functions…

Q: Let f (x) = |x³ + 216|| Find the area A of the region between the graph of f and the x axis on the…

A: Let the function given is  f(x)=|x3+216|

Q: Determine the volume of revolution of the function f(x) = xe 2 Note: you must remember this formula…

A:

Q: Let f(x) = e^(-x) -1 for 0 <= x<= 10 Find the area of the region between the graph of f and the…

A: Use area under curve

Q: Let the region R be the area enclosed by the function f(x) = 2x and g(x) = 3x. If the region R is…

A:

Q: Say the function g(x) = ;x + 2. Approximate the area bounded by the graph of y = g(x) and the x axis…

A:

Q: Let the region R be the area enclosed by the function f(x) = x +1, the horizontal line y = 0 and the…

A:

Q: Find the volume of revolution about the x-axis for the given function and interval: f (x) = 3x − x2,…

A: The volume of revolution about x-axis for a function f(x) in the interval a, b is given by,…

Q: Let the region R be the area enclosed by the function f (x) = x³, the horizontal line y = -1 and the…

A:

Q: Let the region R be the area enclosed by the function f (x) = ln (x)+1 and g(x) = x – 1. If the…

A: The solid is a semi-circle perpendicular to the x-axis. Visualize the region.

Q: Let f (x) = e¯× – 1 for 0 < x < 1. Find the area A of the region between the graph of f and the x…

A: fx=e-x-1,  0≤x≤1

Q: Consider the region below f(x) = x/2, above the x-axis, and between x = 0 and x = 4. Let x, be the…

A: Given the function f(x) = x/2 above the x- axis now x =0 and x =4 are given  so the interval is…

Q: Approximate the area of the region under the graph of the function f on the interval [0, 2] using…

A:

Q: Let the region R be the area enclosed by the function f (x) = g(x) = 7x + 2.Find the volume of the…

A: The functions fx=2ex and gx=7x+2. Then we have to find the volume of the solid generated by revolved…

Q: Let the region R be the area enclosed by the function f (x) = x² – 2 and g(x) = 2x – 2.Find the…

A:

Q: Let the region R be the area enclosed by the function f (x) = x³ +1 and g(x) = x + 1. If the region…

A:

Q: Let the region R be the area enclosed by the function f (x) = ln (x)+1 and g(x) = ;x.Find the volume…

A: Observe that the line gx=12x forms the outer periphery of the solid, while the logarithmic curve…

Q: Find the volume of revolution about the x -axis for the given function and interval f(x)%33x – x²…

A: Given function is

Q: The volume of the surface generated by rotating the function f(x) (* > 1) around the x-axis is А. 2т…

A: The cylindrical shell method is used for calculating volume of revolution.

Q: Let the region R be the area enclosed by the function f (x) = 2 ln (x) and g(x) = 2x – 4.Find the…

A: We have f(x)=2lnxg(x)=2x-4   If the bounded region between the graphs is revolved around y=-5, then…

Q: the volume of f(x) = e^(-5x) and bound by x-axis and y- axis

A:

Q: Let the region R be the area enclosed by the function f (x) = ln (x) and g(x) = x – 2. If the region…

A: To find the length of the side of a square, compute the vertical distance between two curves fx=lnx…

Q: Let f (x) = |x3 + 216| Find the area A of the region between the graph of f and the x axis on the…

A: given area can be found as below :

Q: Let the region R be the area enclosed by the function f(x) = ln(x) + 1 and g(x) = 3/4 * x - 1 If the…

A:

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: We will have to find  qrea bounded by rhe curve  y= x1/2  X=4 and xaixs

Q: Consider the function g (x) = ±x² +1. What is the approximate volume of a solid that is formed with…

A: GIVEN: g(x) = (1/4) x2 + 1

Q: 7. For the function f(x) = cos x, find the net area of the region between the curve 0, and find the…

A:

Q: Let the region R be the area enclosed by the function f (x) = x³ , the horizontal line y = -2 and…

A: The volume for solid of revolution between curves is the volume of the object between a curve f(x)…

Q: Let the region R be the area enclosed by the function f(x) = 2x², the horizontal line y = 8, and the…

A:

Q: Find the volume of f(x) = e^(-5x)  around x

A: Find volume.

Q: Let the region R be the area enclosed by the function f(x)=2ln⁡(x)f(x)=2ln(x) and…

A:

Q: Q4: Solve the follov A) Find and graph the volume generated by revolving the first quadrant area…

A:

Q: Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and g(x) = x – 1. If the…

A:

Q: find the volume of revolution about the x-axis for the given function and interval. f (x) = x5/3,…

A:

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

A: Given f(x)=x2+x-20. Find the area bounded by x-axis and f(x) on [2,5].

Q: Let the region R be the area enclosed by the function f (x) = e¤ – 1 and g(x) = 4x. If the region R…

A: If a region enclosed by the functions f(x) and g(x) over the interval [a,b], and the region is the…

Q: 32.g( (z)=z +1, [1, 3,8 rectangles

A:

Q: Let the region R be the area enclosed by the function f(x) = x², the a-axis and the 2. Find the…

A:

Q: Let the region R be the area enclosed by the function f (x) = 3 ln (x) and g(x) = 2x – 3.Find the…

A:

Q: Consider the following function: f(x) = /3x x2 a. find the endpoints of f(x). b. Find the area of…

A: