a) Find the area of the curve x²/3 +y2/3 = a²/3 %3D

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

A:

Q: 2. Find the area in the third quadrant bounded by the curve x= y2 + 2y.

A:

Q: 15. Sketch the region enclosed by the lines x = 3 and y = 1 and the curve xy = 9, and find its area.

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: 6. Find the area bounded by the curve 2y² + 4x + y = 0 and the line y = 2x.

A:

Q: 3. Find the area bounded by the curves x2 + y2 = 9 and 4x2 + 9y² 36, on the first quadrant.

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Q: 2. FIND THE AREA BOUNIDE O BY 2 y= x (2,4) and the X- axis THE CURVE

A: The given curve is: y=x2      .........(1)We have to find the area bounded by the curve y=x2, (2,4)…

Q: Find the area between the curve y=x^3 and its tangent through (1,1)

A: The slope of the tangent is given by y' at (x,y)=(1,1) y'=3x2At x=1y'=3 Equation of tangent line is…

Q: 1. Find the area bounded by the curve y In x and the %3D lines y = 0 and x = e.

A: Given curve is: y=lnx and the line y=0 and x=e Area of bounded regions: Let y=f(x) be a continuous…

Q: 4. Find the area bounded by the curves y = 2x – x2 and the x-axis

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

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Q: 1. Find the area in the second quadrant bounded by the curve 2x² + 4x +y = 0 using two methods

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Q: Find the area between the curve y = sin 2x and y = x^2

A: the area is 4/5

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: 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: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Find the area of the region bounded by the curve y2-4r and the lines x = 1 and x = 4.

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Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

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Q: Find the area of the region bounded by the curves: y = cos(nx) and y = -1 + 4x2

A: The region between these two curves is shaded below

Q: Find the area between the curve y = sin x and the line segment joining the points (0, 0) and (5π/6,…

A: Consider: y=sin x and line joining the points 0,0 and 5π6,12. Find the area between them.   First…

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 bounded by the loop of the curve y² = 4x²-x*

A: The given equation of the curve is: This can also be written as: The graph of this curve is:

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: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

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Q: Find the area lying between the parabola y = 4x – x² and the line y = x -

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Q: Bm 11 2元

A: we need to find the integral of the function in the given limits to get the

Q: 10. Find the area bounded by the curve x = y² + 2y and the line x = 3.

A: Area Bounded by the Curves : If f(y) and g(y) are two continuous function on a,b and f(y)≥g(y), then…

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

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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: 4. Find the area bounded by the curve r = 3y – y? and the line y + x 3.

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Q: (b) Suppose we wish to estimate the area 3 Vĩ dx 2 using the Trapezium rule.

A:

Q: Find the area of the region lying between the æ- In(9x) – 1 axis and the curve y = to the right x2…

A: Solving by area formula

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: Find the area between the curve y = sec (4x) and the line joining the points (-,2) and (. 2).

A: Consider the given information: To find the area between the curve and the line joining the points.

Q: Find the area b0 und by Curves the y3= X-3

A: The region is bounded by y=9x2-36, y=0, x=1 and x=3

Q: 11. Find the area bounded by the curve y² + 2x - 2y - 3 = 0 and the y-axis.

A:

Q: 9:(a): Find the area bounded by the curve y² = -x, the line y = x, and the line y= 2.

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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 between the curve y = 2x² + 4x-6 and the x-axis from x = -2 to x= 3. %3D %3D %3D

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

A:

Q: 3. Find the area bounded by the curve y 4sin(2x), the x-axis, and the lines x = 0 and x =

A: We have to find the area bounded by the given curves. We will find the area by the help of…

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

A:

Q: Find the area bounded by the given curves. x2 = y - 1 and x = y - 3

A: From the given curve   x2=y-1 ; x=y-3   Now finding the point of intersection for both curves:…

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

A:

Q: Find the area of the region bounded by one loop of the curve x2 y*(1 – y²)

A: Given:          x2=y41-y2         x=±y41-y2         x=y21-y2 The graph is symmetric about the…

Q: Find the area of the region bounded by the curvesr = 2 cos 30 and x = y – 1.

A: The curves given are as follows: r=2cos3θx=y2-1 We know that x=rcos3θ, y=rsin3θ.…

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: Find the area of the region bounded by the curves: y = cos(nx) and y = -1+4x2

A:

Q: 18. Find the area of the region enclosed by the curve y = (1- x)²; 0<x< 1. (in QI)

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Q: Find the area between the curve y = x(x 3) and the ordinates x = 0 and x = 5. LA B

A: Topic = Area

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.