65. The region bounded by f(x) = x² and the x-axis on the interval [1, 0) is revolved about the x-axis.

Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

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Q: (13) Find the area of the region between the line y = 2x and the curve y =x² +x-2 %3D

A: The given two curves are y = 2x y = x2 + x - 2

Q: 1. Find the volume of the solid formed by revolving the region bounded by the graph of f (x) = -x² +…

A: Given problem:- Find the volume of the solid formed by revolving the region bounded by the graph of…

Q: 10. Find the area between y = 3x²+14 and y = 4x + 2 over the interval [-2 , 2]

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Q: 1. Find the area bounded between the curves: y = x+1, y = -2x + 7 and x = 0 A. With respect to the X…

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Q: R is the region bounded by y = 4 – x2 and the x-axis and it is revolved about y = 4.

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Q: What is the total area between f(x)=−6x and the x-axis over the interval [−4,2]

A: Graph of f(x)=-6x in interval -4 to 2 is shown on board

Q: 1) Find the area bounded by curve y = xvx2 + 1 and the lines x = 0, x = 4 an %3D the x-axis.

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Q: 1. Find the area of the region between the curves y=x -4 and y=2-x.

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: I. FIND THE AREA BOUNDED BY THE FF CURVES AND LINES: 1. The loop of y = x *(4 - x) 2. у %3 бх - х, y…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 4. Find the area of the region bounded by y = cos x, y = sin x, x = 0, x = %3| might have to break…

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Q: 1. Determine the area bounded by curves y = -x² + 4x + 3 and y = −x³ + 7x² − 10x + 5 over the…

A: We have to find the area bounded by the curves.

Q: .2 What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis…

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Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x2.

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: What is the area of br^2 of the region bounded by

A: The given question is taken from the calculus in which we have to find the area bounded by the given…

Q: 1. Find the area of the region bounded by the ves y = x³ – 5x + 6, y = 10 – 4x – 4x2 and the line x…

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Q: 3) Find the area bounded by the curves: x² – 4x + 1 = 3y and x2 + 2x + 2y – 5 = 0.

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Q: Volumes Find the volume of the described solid of revolution or state that it does not exist.

A: Given function is f(x)=1x lnx and the interval is [2, ∞).

Q: 14. Find the area of the region bounded by these two curves: X = y' – 2y and x-y-4=0

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Q: The area of the region bounded by the curves y =x and y = 20–x² is попe 4.4 O 4= " |20–x²-x| dr -4.4…

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Q: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 7. Find the area bounded by the curve y = x² + x + 4, the x-axis and the ordinates x = 1 and x = 3.

A: The area under the curve y=f(x) in the interval a, b is calculated using the formula: A=∫aby dx. We…

Q: Find the area under the curve f(x) =x+3x+7, above the X axis from x=4 to x=6.

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Q: 1. Find the area bounded by the curve y = x^2, the x- axis, and the ordinates x = 1 and x = 3.

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Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

Q: 6. Find the area bounded by: d. The curves y=x-4, y38-2x.

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Q: 11 Find the area of the region bounded by y = x² + 2x – 1, y = + x x = -3, x = 1. 2

A: Area between curves

Q: 1. The area bounded by the curves y x2,y 0, x = 2,x = 5 is 39. 2 is 10

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Q: ii) area bounded by x -y = 1, 2x + y = 5and x + 2y = 7 in first quarter is: 20T 21T 22m

A: The area is the measure of the amount of space occupied by the plane figure. It is measured in terms…

Q: 2. Find the area bounded by the curve y = x³ – 3x2 from x = 0 to x = 2. -

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Q: The region bounded by f(x) = (x + 1)-³ and the x-axis on the interval [0, ∞) is revolved about the…

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Q: 5. Given the region R bounded by y = 4-x² and the x-axis, find the horizontal ine y = k that divides…

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Q: 6. Find the area of the region bounded by the two curves of equat rens a) x=3-y² and f(x)= 3x (スー2)-…

A: Note:- In Part (a), you mention f(x) for 2nd curve but it is not mentioned for first curve. If i…

Q: 11. Find the area bounded by the curve y² + 2x - 2y - 3 = 0 and the y-axis.

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: 2. Find the area of the region bounded by x = y² - 4 and x = 3y.

A: Given query is to find the area of the region bounded by x=y2-4 and x=3y. The rule for integration…

Q: The exact area of the region bounded by the graphs of y = x² + 2, and the x – axis from r = -1 to x…

A: Given that:

Q: Areas of regions Find the area of the following regions.

A: Given that, y=10x2-2x-24

Q: 2.) Verify the conclusion of Green's Theorem given F(x,y) = (ye",e") and C is the boundary of the…

A: The objective is to verify the Greens theorem for the given function.  Let C be the positively…

Q: Find the area of the region between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

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Q: 1. Find the area of the region bounded by the graphs of the equation Y = x and y = x2.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 14. (a) Find the area bounded by the curves y = 2x² and y = 4x. %3D (b) Two cars both start on a…

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Q: 1. Find the area of the region bounded by the curve y = f (x) = |a² – 4| and the lines x = -3, and x…

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Q: 2) Find the absolute maximum and minimum for function F(x,y)= 4x³-2x²y+y² on the region R bounded by…

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Q: 3 2. Find the area bounded by the two curves y = x³- 6x² + 8x and y = x² - 4x.

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Q: 7- The area of the (bounded) region between the line y = x quadrant is and the curve y = x² in the…

A: 7) The area of the region between the line y=x and y=x2 in the first quadrant. First we draw the…

Q: 1. Find the area of the region bounded by y = x² - 3 and y = 5 - x².

A: This question can be solved using the concept of area bounded by two curves.