Find the area bounded by the curve and perimeter when r^2= a sin theta (1 + sin theta). Show graph and detailed solution.

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be

Q: Find the area bounded by the curve y=4x-x² and the lines x=-2 and y=4.

A: See below

Q: Find the area bounded by the parabola y2 − 3x + 3 = 0 and the line x = 4. With illustrations please

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Q: Find the area bounded by tHe curves y=8x-x and y= 3x

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Q: The area between the two curves in the picture is

A: GIven functions are, y1=4y2=x2The given graphs are symmetric about y axis.The points of intersection…

Q: The method of washer is used to find the area between curves. True False

A: follow next step

Q: Find the area bounded by the ff. curves and lines: a. arch of y =(1/3)sin(x/3)

A: Consider  the equation

Q: Find the area of the triangular region in the first quadrantvbounded in the left axis by the y axis…

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

A: Given curves are  y2=4x, 2x+y=4 The region bounded by the above curves  is the yellow colored region…

Q: Sketch the region enclosed by the curves and find its area. y = 9x² ,y = 9Vx,x = 1 - and x = 1 Enter…

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Q: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

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

A: The x coordinates for the points of intersection of the curves are given by:…

Q: 4 y = 1 + x4' y = 2x2

A:

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

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Q: Find the area bounded by the curve y²=9x and its latus rectum

A: Given equation is y2=9x the equation of parabola is of the form  y2=4axlatus rectum x=a  and…

Q: Sketch the curve. r = 4 - sin(0)

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Q: Find the area bounded by y = 3x² - 3 and y = 3. Leave your answer %3D correct to 2 decimal places.

A: Given  y = 3x2  -3  and y = 3 To find : Area bounded.

Q: Sketch the region by the curves and find its area. y=x^2 y=x+2

A: Given,

Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: Determine the area of the triangle bounded by the coordinate axes and the tangent to x² - y = 0 at x…

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

A: Solution:-

Q: Sketch the signed area represented by the integral. Indicate the regions of positive and negative…

A: The green region is the positive region while the blue region which is below the x-axis is the…

Q: about the y axis, which integral below giv area?

A: Introduction: The formula for the surface area of the curve rotated about y-axis is given by,…

Q: Find area enclosed by curves y=2x, y=4x^2

A: Area enclosed by two curves is the measure of the area occupied by their intersection.

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: Therefore, the value of the integral is 0.23286.

Q: Write expressions for the area enclosed by a curve interms of line integrals around .

A: Green's theorem transforms the line integral around C into a double integral over the region inside…

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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Q: find the area enclosed by the graphs in two ways: by integrating along the x-axis and by integrating…

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Q: Find the area bounded by y = 2x2 - 4 and y = 5. Leave your answer correct to 2 decimal places.…

A: This is area under the curve problem

Q: Find the area bounded by the curves y=sinx, y=cosx between x=0 and x=π/2. PLEASE INCLUDE HOW TO GET…

A: To find out the area bounded by the curves.

Q: Sketch the region enclosed by the given curves and find its area. x = y4,  y = square root of (2 -…

A: We first sketch the region using a graphing calculator

Q: Sketch the region enclosed by the curves: y= x^2-1, y = 7-x^2. Then set up (but do not evaluate) the…

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Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

Q: Find the area under the curve  y= (2x2 - 7) / (sqrt(x)) ,   16 <= x <= 20

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Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

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Q: 2. By integration, show that the area of a circle of radius r is A = rr?

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Find the area between the curves.

A:

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

A: The given parabola is: y=2x2 The tangent line at (5,50) has the slope: mx=5=dydxx=5          =4xx=5…

Q: h -y =

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Q: 5. x-y(2-y) and x=-y

A: The given curves are; x=y2-y and x=-y Now find the point of intersection between the given curves.…

Q: Calculate the area of the area between the curves

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Q: Find the area of the region bounded by the curve y= 1--x² and the x-axis.

A: Given equation of the curve: y=1-19x2 To find: Area of the region bounded by the curve and x-axis.

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.  Show full complete solution.

A: Given : Curve : y²= 4x              and line  2x+y=4 To find : Area between the curve and line

Q: Find the area bounded by the curve x = ý +2y and the line x = 3.Use horizontal strip.

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Q: Find the area bounded by the curves

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Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

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Q: how do I determine the area under a curve?

A:

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.