Find the area of the region                  Inside one loop of the lemniscate r^2 = 4 sin 2u

Q: Compute the rotated area bounded by y = 2x, x = 2 and x-axis about x-axis

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Q: Find the area of the region bounded by the graphs of the equations.

A: Given that : The curve y = 4x2 + 3 , x = 0 , x = 2 , y = 0.

Q: Sketch the region enclosed by the curves and find its area. 1 х — 0, у — 1, у — е NOTE: Enter the…

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. + dx -2

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Q: an arch of y = sin() %3D

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Q: Find the area of the region bounded by: r = 5 – 3 sin 0

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Q: Find the area of the region enclosed by one loop of the curve r = 4 sin(7theta)

A: Loop:- A curving or doubling of a line so as to form a closed or partly open curve within itself…

Q: Sketch the graph the integrands and use areas to evaluate the integrals. | Ix| dx -2

A: Follow the procedure given below.

Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum.

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Q: Sketch the region of integration for the double integral given by ∫20 ∫ex0 dydx and change its order…

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Q: What is the area of the region bounded by the graph of r = 4 sin 2θ

A: What is the area of the region bounded by the graph of r = 4 sin 2θ

Q: Find the integral of ∫(sin2x - cos2x)2dx. Use trigonometric transformation or integration by parts.

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Q: find the Curve A the region enclosed by ye Sin (ITx/2) and the the area line

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Q: Sketch the region bounded by the given curves, then find its area. y = 12 - 3x^2, y = 4 - x^2

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Q: Sketch the region and use a double integral to find its area. The region bounded by the cardioid r=…

A: The cardioid is r=-31-sinθ, θ r=-31-sinθ 0 r=-3 π6 r=-32 π4 r=-31-12 π3 r=-31-32 π2 r=0…

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: Find the area by using double integral in polar coordinate. /4

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Q: Sketch the graph the integrands and use areas to evaluate the integrals. LV16 – x² dx

A: Here we have to use areas to evaluate the integrals.

Q: Sketch the graph the integrands and use areas to evaluate the integrals. V16 – x² dx

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Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Find the area of the region bounded by the graphs of the equations               y = cos2 x, y =…

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Q: how to find  Find the area of the region enclosed by one loop of the curve. r = sin(4θ)

A: The given curve is r= sin4thetaArea of the curve enclosed in the first loop is,

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: 2- Region enclosed by the cardiaid (r=\- Sin@)in 1-st quadrant.

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Q: Find the area of the region cut from the first quadrant by the curve r = 2(2 - sin 2u)^(1/2).

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Q: Find the area of the region bounded by the 3 graphs of the equations y = sin x, y = sin° x, 0, and x…

A: Consider the given curves. Equate (1) and (2) and calculate the x where (1) and (2) are equal.

Q: Sketch the region enclosed by y=4x and y=3x^2. Find the area.  Im having trouble showing my work to…

A: Find the area bounded by the 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: Compute the area of such region: (in picture) and sketch it.

A: Compute the area as follows.

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

A: Solution:Given  Let         I=∫-11tan-1xdxTo sketch th signed area represented by the integral and…

Q: Calculate the area of the region bounded by the graph of f(0) = cose sine and the 0 - axis between 0…

A: Consider the given function: fθ=cosθsinθ Area of a function fx in interval a,b is given by:…

Q: 10.4-#33

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Q: Evaluate the integral. sec do %3D

A: According to guidelines we are supposed answer only first question if you want any particular…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: 6. у%3D х2 —Зх, y = x

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Q: find the volume of the object obtained when one rotates the area under f(x) = cosx²)and over 0 <x< =…

A: Given, fx=cosx2  ,0≤x≤π2 The formula for finding the volume of the function fx is, ∫abπfx2dx

Q: Sketch the region bounded above by the curve 7e- sin(Tx), the x-axis, and x = 1, and find the area…

A: Given,

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y…

A: Let's find area enclosed by given  curves.

Q: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

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Q: Find the area of the region bounded by the curve r^2 = 16cos theta. show full solution

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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: Sketch the region of integration and evaluate the integral of :

A: To evaluate and sketch the region of integration of, ∫03∫024-y2dydx

Q: Find the area of the region enclosed by graphs of the functions y=sin(8x) and y=sin(16x),π/24⩽x⩽π/8

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Q: Use double integration to find the area bounded by the given curves

A: Note: since you posted multiple question, as per our guidelines we are supposed to solve one…

Q: Find the area of the region between the curves

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Q: Find the area of the region enclosed by one loop of the curve. r=sin(8theta)

A: Draw the given curve as shown below.

Q: Find the area of the region shaded below that is inside of a circle of radius 4.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the area bounded by the circle r = 2 sin 8 and r = 4 sin 0.

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Q: Graph the integrand and use areas to evaluate the integral. dx -1

A: ∫-11(1+1-x2)dx

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.