1. Find the area of the trapezoid that is the region bounded by the lines x = 1 and x = 3, the x axis, and the line 2x +y = 8. Take an inscribed rectangle. 2. Find the area of the region bounded by f (x) = 4– x2,the x-axis, and the vertical lines x = 1 and x = 2. 3. Find the area under the line y = x, x - axis, and the lines x = 0 and x = 1.

Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: The area bounded by the curve y = x*, x- axis and the lines x=1 and x=2 is_ O A. 21 5 О в. 31 5 ос.…

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Q: 2) a) Consider a rectangle which is on the region bounded by the lines y=x+4, y=-x+4 and X – axis.…

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Q: Find the area bounded by the curves 5y^2 = 16x and the curve y^2 = 8x – 24

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Q: Find the area of the region bounded by the graph ofy =1/x the x-axis, and the vertical lines x = 1…

A: The area is calculated by taking a rectangular element of width  dx and height y. The total area is…

Q: Find the area A of the region between the graphs of the equations y² = 3x x2 = 3y

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Q: Consider the region bounded by the graph of y = 4x + 3, the x-axis, and the lines x = 2, x = 7. A…

A: Given area bounded by the curve y=4x+3, x-axis and the lines x=2, x=7

Q: 2) a) Consider a rectangle which is on the region bounded by the lines y = x+4, y =-x+4 and X -…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let R be the region bounded by the x-axis, the graph of y = Vx , and the line x = 4. Find the value…

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Q: The area under the curve y = 3x bounded by the lines x = 3 and x = 8 above the х — ахіs is. - 192.00…

A: we have to find the area bounded by the given lines

Q: In the given equation  find a such that the line x a divides the region bounded by the graphs of the…

A: Given, y=x,y=4,x=0     Find a value of a such that the line x=a divides the region bounded by the…

Q: Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| and y =…

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Q: 13. Find the number b such that the line r = b divides the region bounded by the lines y = 1, y = 2x…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 6. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area…

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Q: 1. Find the areas enclosed by the y-axis and the following curves and straight lines: b. x= y(y-2),…

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Q: 1- Find the areas of the regions enclosed by the lines and curves: y=r-2 and y= 2 1- y = x* and y =…

A: As per the guidelines we can solve 2 problems only

Q: d) Let A, be the region between y = x² +9 and y 21-x. Let A, be the region between y = x² + x – 12…

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Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: 1- Find the area of the region enclosed by the line y=4x and the curve y=x'+ 3x'.

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: Find the number  b such that the line  y = b divides theregion bounded by the curves y = x 2  and y…

A: Given Data The equation of curve is y=x2. The equation of line is y=4. The equation of another line…

Q: In the given question  find b such that the line y b divides the region bounded by the graphs of the…

A: Given :           Equation of curves as :                  y = 9 - x , y = 0 Formula :           A =…

Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: Find the area bounded by the ff. curves and lines: a. y = xe^–x , the x-axis and the maximum…

A: To find the are bounded by the curves and lines: (a) y=xe-x, the x-axis and the maximum ordinate.

Q: The base of a three-dimensional figure is bound by the graph x = y³ and the y-axis on the interval…

A: In this question, we need to find the area of each rectangle and not the area of the complete…

Q: The area under the curve y = 5x bounded by the lines a = 3 and æ = 6 above the a – axis is_ 225.00…

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Q: Find the area of the region bounded by f(x) =|x^2−5x+ 6|, the x-axis, and the lines x=1 and x= 4.

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Q: What is the area of the region in the first quadrant bounded above by y = -2x + 8 and below by y =…

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Q: 3. Determine the area to the right of g(y) = y2 + 4y – 5 and to the left of the y- axis.

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Q: 1. The area of the region enclosed by the x-axis, the curve y = f(x) > 0, and the lines x = to f³(b)…

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Q: 7. Find the area of the region bounded above by the line y 3, below by the graph of y VT, between…

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Q: 30. Find the area bounded by the curve 5y²=16x and the curve y²=8x-24. A. 36 B. 25 C. 16 D. 14

A: Topic = Area

Q: A region bounded by f(x) = x² + 1, y = 1, and x = 2 is shown below.

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Q: Find the area of the region bounded by y = -4x + 9, y = 2x? – 11x + 9, and the lines x = -2 and x =…

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Q: The base of a three-dimensional figure is bound by the line y = 4 - x on the interval [-2, 2].…

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Q: 1- Find the area of the region enclosed by the line y=4x and the curve y= x³ + 3x².

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the total area of the regions enclosed by the two curves y = 4-x2 and y = -x+2 %3D and the two…

A: The given curves are: y=4-x2, y=-x+2 and the lines x=-2, x=3

Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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Q: Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area of…

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Q: Find the area bounded by the x-axis, the curve y = x² and the vertical line x = 3. and Find the area…

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Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

Q: (b) Find the areas of the regions enclosed by the line y = x and curve y = x- 3x

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Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: The area bounded by the curve y 3x and the lines x = 4 and x = 36 above the x – axis - is O 3888.00…

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Q: (b) Find the areas of the regions enclosed by the line Y=* and curve y=x-3x

A: Given: Curves y=x and y=x2-3x Definition: The area between curve f(x)≥g(x) on the interval [a, b] is…

Q: The area bounded by the curve y = 3/x and the lines x 3 and x = 8 above the x axis is _square units…

A: All options are incorrect.

Q: 2. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

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Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

Q: 5. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3 Then the area…

A: We know  that the area under the graph of a continuous function f (x) between the vertical lines x =…

Q: 7. Determine the area to the right of g(y) = y² + 2y – 4 and to the left of the line x = -1.

A: By using area between the curve formula, We calculate the required area.