4. Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the curvex = 2,/y and above by the curves x (y- 1) and x 3 - y.

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Find the area of a region bounded by the curves y=e^(2x) - x^3 , the y-axis and x=1

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Q: 1/ Find the area of the region enclosed between the curves y= 2r'+10 and y=4x+16 and ,x=-2 and x=5?…

A: The area of the region enclosed by the given curves has been obtained below.

Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

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Q: 3. Find the area of the region in the first quadrant that is bounded above by y = vx and below the…

A: Solution

Q: 1. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

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Q: 2. The area bounded by y=3x+4 and the curve y=x2 is revolved about the line x =5.

A: 2) The area bounded by the given curves is:

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

A:

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: Find the area of the curve y = x° – 2x – 3 between x =- 1 to x = 3.

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Q: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: 9. Find in two ways the area bounded by the parabola y = x², the y-axis, and the lines y = 1, y= 4.

A: Given,  The parabola y = x2  We have to find the area bounded by the parabola, y-axis and the lines…

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

A:

Q: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

A:

Q: 26. Find the area of the region bounded by the curve y = 4x – x?, the lines x = 1 and x = 3 and the…

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

A: We have to compute the area between the given curves using the double integration method by first…

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: Find the area of the region bounded by the parabola y = 2x, the tangent line to this parabola at (4,…

A: Definition used -              Equation of a tangent line -                  (y-y1)=f'(x1)(x-x1)…

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: B- Find the area between the curve (y-√x - 2) and the lines (y-4-x),(y=0).

A: We have given three curves-y=x-2y=4-xy=0 First we will find intersection of first two curves…

Q: 2. Find the area in the second quadrant bounded by the curve y = x' +4x² –x-4 and the x- axis.

A: To find: The area in the second quadrant bounded by the curve. Given: The equation of the curve is…

Q: Find the area bounded by the curve 5y2 = 16x and the curve y2 = 8x − 24 and provide a correct and…

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Q: 1. Find the area between the curves x2-y = 9 and the line y 2x-6

A: Since you have posted multiple questions in this question which are not interlinked so I do only…

Q: 1. Find the area between the curves x2-y2 = 9 and the line y = 2x-6

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Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

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Q: Find the area of the region bounded by the parabola y = x², the tangent line to this parabola at (1,…

A: Given data: The equation of the parabola is y=x2. The given point is (a, b)=(1, 1). The slope of the…

Q: 1. Find the area bounded by the curves y – 2 = x² ,y = 6 and the y – axis ( in Quadrant I only), as…

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Q: 1/ Find the area of the region enclosed between the curves y= 2r²+10 and y=4x+16 and ,x=-2 and x-5?…

A: Given          y=2x2+10    and  y= 4x+16,   x=-2 and   x=5.

Q: 1/ Find the area of the region enclosed between the curves y= 2x2+10 and y=4x+16 and ,x=-2 and x=5?…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. Find the area of the region bounded by the curves y = x2 – 3x + 5 and y = 3x + 5.

A: Answer and explanation is given below.. For solution of other questions please repost

Q: Find the area between the curves: y2=x x2– 2x + 3y = 2

A: we have to find the area between the curves :

Q: Find the area between the curve y=2x+4x-6 and the x-axis from x =-2 to x= 3.

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Q: Find the area of the region bounded by the parabola y=x2 , the tangent line to this parabola at…

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Q: 2. Find the area enclosed between the curves y =x² +2x +11 and y =-4x+2.

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Q: 7. Find the area of the region under the curve y= |2x – 1| between x= O and x= 2.

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Q: A\ Calculate the area of the segment cut from the curve y =2x2 by the line y = x+1 with x2 0.

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Q: - Determine the area bounded by the curves y = -1² – 16x + 80 and y = (x – 4)°.

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Q: Find the area of the region bounded by the parabola y = x2, the tangent line to the parabola at the…

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Q: Find the area of region bounded by the curves x= 2y+6 and x y-1.

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Q: 1)Find the area bounded by the given curves: a)y = 6x2 and y = 24   b)y = 3x2 − 12 and y = 0

A: The given function are y=6x2 and y=24. The area bounded by the given curves as shown below:

Q: 1. Find the area between the curves x2-y 9 and the line y 2x-6 %3D

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Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

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Q: Find the area of the region bounded by the parabola y = 2x², the tangent line to this parabola at…

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Q: Find the area between the curves y -0.2x e and y = 2.4x +1 from x=0 to x=2

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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: Sketch the graph of the given curves and find the area of the region bounded on the left by the…

A: Graph of x=3-2y2, that is gy=3-2y2 is a parabola as function g(y) is in the form of quadratic…

Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

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

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Q: Calculate the area of the following regions bounded by the curve y = 2 - and x = 2y2.

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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.

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.