Find the equation of the vertical line that divides the area of the region R bounded by 1 y = 20x2 and 18 in half. y = x, y = (Round your answer to 4 decimal places.)

Q: Find the area of the region in the first quadrant bounded by the line y=2​x x=4​ y=2/x and the​…

A: The given region is bounded in first quadrant by following curve: y=2xx=4y=2x and the x-axis.…

Q: Find the area of the region bounded by the line y=x, x=2 and by the curve y= (1/x2)

A: Area of the region shaded below÷

Q: The area of the region bounded by y = v9 – x² , the x-axis and the line y=x in the first quadrant…

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

Q: Find the area of the region bounded by the three curves y = x^2 , y = 8−x^2 , and 4x−y + 12 = 0.

A:

Q: The area of the region bounded by y = v9-x² , the x-axis and the line y3x in the first quadrant is:

A: The area of the region is calculated by the double integration, and to solve double integration we…

Q: Determine the area of the region bounded by the curve y = x³ – x² – 2x, and а. the x-axis b. the…

A: Note: As you asked only part (b) so, I answered here only part (b).

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

A: We have to find the area .

Q: Find the area bounded by the curve x^2 + 4y - 8 = 0, the x - axis, and the lines x = 3 and = 5

A:

Q: Consider a region in the first quadrant bounded on the left by the y-axis, below by the line y =…

A: The given region lies in the first quadrant. It is bounded on the left by the y-axis whose equation…

Q: 3 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

A:

Q: FIND THE AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

A:

Q: Determine the area of the region bounded by y = xvx2 + 1, y = 1 e 2x, x = -3 and the y-axis. %D

A:

Q: Find the line y = mx that divides the area under the curve y = x(1 − x) over [0, 1] into two regions…

A:

Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

Q: Compute the area of the region which lies to the right of the parabola x = y^2 – 12 and to the left…

A:

Q: Find the area of the region bounded by y = 3x + 10, y = -4x + 1 and x = 12. Leave your answer…

A:

Q: Find the area of the region which is bounded by y = sin x - 3, y = 3x, y-axis and x = 2. Leave your…

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

Q: The area of the region bounded by the curve y= e", the x-axis,'the y-axis, and the line x 2 is equal…

A: We have to find the area of the region bounded by the curve y=e2x , the x-axis, y-axis and the line…

Q: The area of the region bounded by y = v9- x² , the x-axis and the line y-x in the first quadrant is:

A:

Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 3. Leave your…

A: Area bounded by the given curves :If f(x) and g(x) be two continuous function on a,b and f(x) ≥g(x)…

Q: Find the area of the region bounded by the graphs of the equations. y = Vx(1 – x), y = 0

A: we have y = x(1-x) clearly x≥0we find area of the region        y≥0 if 0≤x ≤1and  y≤0 if x≥1…

Q: = Find area of the region bounded by x² + y² = 4², 10y = -6x and 13y 8x where y > 0. Leave your…

A:

Q: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: find the area of the region bounded by the curve y^2=x+1 , both by the x and y axes and the line x=8

A: Using Reimann sums, the area of the region R is given by Sn=∑k=1n∆Ak. This is simply the sum of…

Q: Find the area of region enclosed by the curves. Hint: using integration y=lx²-4l and y=(x²/9)+4

A: The area under the curve: - Three easy procedures are often accustomed to figure the realm…

Q: Find the volume of: the area bounded by the curve y2 = 9x and the line x = 4 revolved about x = 4.

A:

Q: 3 Find the area of the region bounded by 2x = y²+1 and the y-axis using the horizontal strip.

A: The given region is bounded by 2x=3y2+1 and the y-axis.

Q: Solve by integration: What is the area of the region enclosed by the curve y=x^2 and the lines…

A:

Q: Find the distance of the centerof gravity of the area on the first quadrant region bounded by the…

A:

Q: Find area of the region bounded by x² + y² = 5², 7y = -3x and 19y = 4x where y > 0. Leave your…

A:

Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

A:

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: Determine the area bounded by the curves y = -² – 20z + 96 and y= (r – 4)?.

A:

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 graphs of the equations. y = Vx(4 – x), y = 0

A: Given: The equations are y=x4-x  and  y=0.

Q: Determine the area of the region bounded by y = xvx2 + 1, y = 1 e 2x, x = -3 and the y-axis.

A: First draw the region defined by these curves. If the region is bounded, then use the area under the…

Q: Find the area of the enclosed region bounded by the graphs of y=e^x, y=x, the y-axis and the line…

A: Here we have to find the area of the enclosed region bounded by the graphs of y=ex,y=x,the y-axis…

Q: Determine the area bounded by the curves y = -r - 18z + 40 and y = (x- 2)2.

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Q: Find the area bounded by the curve y^2 + x - 4y = 5 and the y-axis. Input only the numerical value…

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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…

A:

Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 4. Leave your…

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

Q: Find the area of the region bounded by y = 7x + 7, y = -9x + 4 and x = 15. Leave your answer correct…

A: The solution of the problem is given in the next steps.

Q: Find the area of the region between the curve y = √2x — 1 and the lines x = 1 and x = 5.

A: Given: The region between curve y=2x-1 and lines x=1 and x=5

Q: Find the area of the region bounded by the curves y = (x+8)2 y = 4 and the x-axis using vertical…

A:

Q: Find area of the region bounded by x² + y² = 42, 9y = -10x and 14y 5x where y > 0. Leave your answer…

A: Given: The area of the region bounded by the curves are x2+y2=42, 9y=-10x, 14y=5x where y≥0 To find…

Q: Find the area of the region bounded by the graphs of the equations. y = Vx(4 - x), y = 0

A: Sketch the area of the region bounded by the graphs of the equations y=x4-x and  y=0 as shown below.…

Q: 48. Bounded by the curve y = 2/, the æ-axis, and the lines æ = 0 and æ = 16

A: Area under curve

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.