Consider the graph of the cubicy = x(x - a)(x - b), where 0 < a < b. Verify that the graphbounds a region above the x-axis, for 0 < x < a, and bounds aregion below the x-axis, for a < x < b. What is the relationshipbetween a and b if the areas of these two regions are equal?

Q: Find area of the region enclosed by the parabolasy = 4x – x² and y = x2 - 4x. %3D ation of the eu…

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Q: Consider the region bounded by the graphs of y = x2 and y = b, where b &gt; 0. Sketch a graph of the…

A: The given graphs are y=x2 and y=b, where b&gt;0 we have to sketch the region bounded by the graphs…

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: In the given question , use the Midpoint Rule with n = 4 to approximate the area of the region…

A: We have to use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the…

Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its…

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: Find the areas of the regions enclosed by the curves x + y2 = 3 and 4x + y2 = 0

A: Given The equation of curve is  x + y2 = 3 and 4x + y2 = 0  To solve both equation for x . x = 3 -…

Q: In the given question , find the area of the region bounded by the graphs of the equations:-   y = 1…

A: Given : The equations y = 1 - x4 , y = 0 .

Q: A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50…

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Q: 4. Find the area between the parabolas y2 = 4ax and x² = 4ay.

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Q: The area of the region enclosed by the two curves y=x²-4 and y = x - 4 is given by

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Q: Sketch the region in the xy-plane defined by the inequalities x - 5y2 > 0, 2 – x – 9\y| > 0 and find…

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Q: Find the values of such that the area of the regionbounded by the parabolas  y  = x 2 - C 2  and…

A: given : the two parabolas are: y=x2-C2y=C2-x2 the area bounded by the parabolas is 576.

Q: A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50…

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Q: EXAMPLE 2 Find the area of the region R enclosed by the parabola y = x² and the line y = x+ 2.

A: We have to find area

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: Find the area of the region bounded by the hyperbola 9x2 - 4y2 = 36  and the line x = 3

A: Let the graph of the area of the region bounded by the hyperbola 9x2-4y2=36  and the line x = 3 is,

Q: 1. Find the area of the region bounded by the line y=x+7 and the parabola y=x^2+4x+3 and also…

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Q: 2. The region between the graph of y = 4 - x² and the x-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: Find the values of c such that the area of the region bounded by the parabolas y = 4x2 - c2 and y =…

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Q: Find c 0 such that the area of the region enclosed by the parabolas y- x- c and y = c-a2 is 100.

A: Given the region enclosed by the curve y=x2-c2 and y=c2-x2 To find the value of c such that area of…

Q: 7 Find the area of the region bounded by the a graphs of f(x) = x+ 2x+1 and gix) = 3x+3. Write…

A: The given curves are: f(x)=x2+2x+1          and          g(x)=3x+3

Q: Find the area of the region enclosed by each group of curves. ƒ(x) = x2 - 4x, g(x) = x - 6

A: We find the intersection points of f(x) and g(x) as, x2-4x=x-6⇒x2-4x-x+6=0x2-5x+6=0⇒x-2x-3=0⇒x=2, or…

Q: The shaded region between the graphs of 2x2 + 20 and y = 3x – 15 is displayed - - below in orange.…

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Q: Sketch the region bounded by the graphs of 6x+4y=14 and 4y+6x-2=0, then find its area.

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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: Find the area of the region included between the parabolas y² = 4(p+1)(x + p + 1), and y² = 4(p² +…

A: As per the question we are given two parabolas defined as : P1  :  y2 = 4(p+1)(x+p+1) P2  :  y2 =…

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: Find-the-approximate area-of-the-region-bounded-by-the-curves y = x/Vx2 + 1•-and-y x4 - x1 %3D

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Q: 1) Determine the area of the largest possible rectangle whose base is on the x-axis and the top two…

A: Given the rectangle whose base is lies on x axis and the top two corners lie on the curve y=9-x2

Q: The shaded region between the graphs of y = -2x + 20 and y = 3z- 15 is displayed below in 25 H

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Q: y = x2-4r + 5 y y=x +5

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Q: Sketch the region bounded by the graphs of 6x+4y= 14 and 4y+6x-2=0, then find its area.

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Q: y = -a(x – h)? +k (-2.1 , 2.9) (1,n)

A: The given curve is y=-ax-h2+k. Here h=-1 and k=11 given. So the curves becomes y=-ax+12+11. Also the…

Q: A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50…

A: It is given that radius of circle is 50 feet.  The equation of the region is x2+y2=502; x≥0 and y≥0.…

Q: Sketch the region in the xy-plane defined by the inequalities x- 5y 2 0, 2 - x - 9lyl 20 and find…

A: Graph of the curves÷

Q: 3- Find the area between the parabola x² = 4y and the straight line x-2y + 4 = 0

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Q: Suppose that candy costs $4 per pound and cashews cost $5 per pound. Let x be the number of pounds…

A: We have given,Cost of candy = $4 per poundCost of cashews = $5 per pound

Q: Q1: The area of the region bounded by the graph of y=-0.5x+4and y=3x in first quarter.

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Q: Find the area of the region bounded by the semicircle with the equation y = √(4- (x + 2)^2 ) + 1 and…

A: Given region is bounded by curves, y=4-x+22+1y=x2+4x+1

Q: Find the exact area of the region bounded by the graphs of y = x2 -4x+3 and y = -x2 +2x+1. Also…

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Q: Determine the area of the region bounded by the following graphs: x = 1, x = 4, y =-x² + 3x and y…

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Q: Find the area of the donut-shaped region bounded by the graphs of (x - 2)2 + (y + 3)2 = 25 and (x -…

A: It is given that the equation of two circles are x-22+y+32=25…

Q: Find the are of the region bounded by the graphs of the given equations f(1) = 5x² and h(x) =r² + 1.

A: To find: The area of the region bounded by curve fx=5x2 and hx=x2+1. Formula used: The area of the…

Q: Find the value of c > 0 such that the area of the region bounded by the parabolas x² - c and c2 -x²…

A: Sketch the region and integrate in x variable.

Q: Find the area of the region bounded by the graphs of the given equations. b) f(x)=2x2-6x+5,g(x)=x2+…

A: See below the answer and calculation

Q: f the region bounded by the curves y = x3-8x2

A: The region bounded by the curves are y=x3-8x2+20x , y=-x2+8x…

Q: Find the area of the region bounded by the curve y = x³ – 2x² – x + 2 and the x-axis for -1 <x<2, as…

A: We will solve this question by using double integration. where,  y=0 and y=x3-2x2-x+2 and x lies…