Find the total area of the regions enclosed by the two curves y = 4-x2 and y = -x+2 %3D and the two lines r = -2, and r = 3. y = 4 - x2 x = 3 x = -2 y = -x + 2

Q: Find the area of the region between the graph of y=x+2, above x-axis, and between the lines x= -1…

A: Given:

Q: Find the area bounded by the curve y = - -x³x²+3x and the line y=x. 16 4 (A) 10 square units B 8…

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Q: Calculate the total area of the region bounded by the line y= 6x^2 + 9, the x-axis and the line x =4…

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Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: It is given that, y=16x2y=9   Area under the bounded region can be calculated by using,…

Q: Find the area of the region bounded by the curve  y=2x2-3x+2  x axis and vertical lines x=0 and x =…

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Q: 4. Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: Find the area between the curves (x^2)-(y^2)=9 and the line y=2x-6

A: Recall: Area between two curves:          A=∫abf(x)-g(x) dx           OrA= ∫abUpper function-(Lower…

Q: Find the area of the region bounded by the graph of f(x) = x² + 1, the x-axis and the vertical lines…

A: Explanation of the answer is as follows

Q: Find the area of the region in the first quadrant that is bounded above by y = √x and below by the…

A: Now the diagrammatic representation of the area is,

Q: Find the total area of the region enclosed by the curve x = y^(2/3) and the lines x = y and y = -1.

A: To determine the area bounded by the curves.

Q: Find the area of the region in the first quadrant bounded on the left by the​ y-axis, below by the…

A:

Q: Find the area of the region bounded by y=x^2-6x+5, y=0 and the lines x=2 and x=5

A: We have to find the area of the region bounded by y=x2−6x+5, y=0 and the lines x=2 and x=5. The…

Q: Find the area of the region in the first quadrant bounded on the left by the​ y-axis, below by the…

A:

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

A: Given:          y=2x and the curve y=x2+x−2

Q: over the triangular region Cut from the * quadrant by the line x+y =1.

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

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Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: Given,

Q: Find the total area of the shaded region (area constrained by curves) y = -2r4 -2

A: The area of the shaded region is given by  ∫abf(x)-g(x)dx Where a and b are limits of x f(x) and…

Q: The area bounded by the parabola y = 4x2, y-axis and the lines y = 1, y = 4 is

A:

Q: Given y = 3x –- 2x +1, y =-x² + 2x +1 and a straight line y = 0.5x ; where x>0, 1. Sketch the curves…

A: Given y=3x3-2x2+1  , y=-x2+2x+1 and a straight line y=0.5x. We need to : 1) Sketch the curves and…

Q: Find the area of the region bounded by the x-axis and the lines x =- 2 and y =- 4x + 20.

A: It is known that area of region bounded by the curves is given by the integral, A=∫abf2(x)-f1(x)dx…

Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: Find a horizontal line y = k that divides the area between y = x and y = 4 into two equal parts.

A: Solution:Given     y=x and y=4T o find a horizontal line y = k that divides the area between y = x…

Q: Find the areas of the regions enclosed by the curves x3 - y = 0 and 3x2 - y = 4

A: The given curves are x3-y=0   and  3x2-y=4. Rewrite the above equations as  y=x3  and  y=3x2-4. Now…

Q: Graph the equations and shade the area of the region between the curves x = −7 + y2 and x = 5y − y2.…

A: The given curves are: x=-7+y2     and     x=5y-y2

Q: Find the area of the region enclosed between the curves defined by the equations y = x² – 2x + 2 and…

A: Solve the following

Q: Find the area of the region bounded by the line y = 4 - 2x and the coordinate axes.

A: Given query is to find the area bounded by the line.

Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: Find the total area of the region between the curve and the x-axis. 9) y = (x + 4)3; 0 <x<3

A: The Area Under a curve The area under the curve between two points can be found by a definite…

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

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Q: Find the number b such that the line y = b divides the region bounded by the curves y = 9x² and y =…

A: Given, The curves are y =9x2 y =25 y = b Let's draw the curve y =25 and y = b are straight lines…

Q: Find area of the region under the curve y = 3x³ – 5 and above the xt-axis, for 2 < x < 5. area =

A: Graph of the equation:

Q: How many square units is the area of the region bounded by the two curves y = x^2 - 4x and y = x^3 -…

A:

Q: Find the number b such that the line y = b divides the region bounded by the graphs of y = 9x2 and y…

A: To find the number y=b that divides the region bounded by the graphs of y=9x² and y=16 into two…

Q: Find the total area of the region between the curve and the x-axis. 7) y = 2x - x2; 0 sx<2

A: Given, The curve  y = 2x-x2   ;  0≤x≤2 We have to find the area of region between the curve and the…

Q: Find the area of the region bounded by the  graph y=2x2-3x+2 the x axis and the vertical lines x=0…

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Q: Find the area of the region bounded by the curve y^2 = 4x and the lines x = 1 and x = 4.

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Q: Find the area enclosed between the x-axis, the curve y= (x-15)(7-x)(x+12) and the lines x=-12 and…

A: We have to find the area enclosed between the x-axis, the curve y=(x-15)(7-x)(x+12) and the lines…

Q: Find the area enclosed between the line y 1 and the curve y = x2 – 4x + 4.

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Q: Find a horizontal line y = k that divides the area between y = x² and y = 9 into two equal parts.

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Q: Find the equation of a horizontal line that equally cuts the area bounded by the curves 2y=x^2 and…

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Q: Find the area of the region in the first quadrant bounded by the line y=5​x, the line x=5​, the…

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

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Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

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

A: Given: y = 9 - x2,  y = 0 To find: The value of b such that the line y = b divides the region…

Q: Find the region bounded by y=2sqrt(x-1), the x-axis, the line x=5 and the line x=17.

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Q: Find the area bounded by the given curves. y = 4x3 + 5 and y = 4x + 5        square units

A: We first sketch the area using a graphing calculator  There are two areas. They are symmetric. So…

Q: find the total area between the region y=3x^2-3, -2&lt; x &lt; 2 and the x axis

A: