Done Find the area between a large loop and the enclosed small loop of the curve r = 4 + 8 cos(30). >

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Q: /Find the area under the curve y = sin x cos 2x from x=0 to x =-

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2. Find the area which is inside the first curve and outside the second. r= 4(1+sine) r= 4

A: We will use the formula of polar coordinates of integration for calculating the area of the region…

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A: Given,

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Q: Find the area of the region that lies inside both curves

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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 of the region enclosed by the inner loop of the curve. r = 4 + 8 sin(0)

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Q: Find the arc length of the graph of the function y=ln(cosx)y=ln(cosx) over the interval…

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Q: Find the area which is inside the first curve and outside the second. r = 4(1+sine) r = 4

A: To find the area of the region

Q: Find the exact area inside the curve defined by r = 2 + 3 sin 0 and outside the circle r = 2.

A:

Q: Find the area which is inside the first curve and outside the second. r = 5sine r = 2 + sine

A: Given:          r=5sinθ         r=2+sinθ   Area of circle A=πr2              =522π…

Q: Find the area bounded by the curve r = 2 - cos 0.

A: The equation of curve is given as , r=2-cosθ Find the area bounded by the curve.

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Q: Find the area bounded by the curve r2 8 cos 0. %3D

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Q: The area between the two curves in the picture is y = 4 y = x2 dy- | dx x 2 32/3 O

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Q: Find the area between the curves y = cos x and y=−sinxfrom 0 to π/2:

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Q: 4. Find the area of the region that lies inside the curve r = 1 – sin 0 and outside the curve r = 1.

A: It is required to find the area of the region that lies inside the curve r=1-sinθ and outside the…

Q: Find the area of the region enclosed by the curve x = 12 cos(t) – 6 sin(2t), y = 5 sin(t) with 0 <t…

A: Given parametric curve, x=12 cos (t)-6 sin(2t), y=5sin(t) with 0≤t≤π

Q: 2. Find the area of the region bounded by the curve r = 2 cos 30 .

A: Given problem:- Find the area of the region bounded by the curve r = 2cos(3θ)

Q: Find the intersection area between r = 3sine and T = 2 - sine curves.

A: given, r=3sinθ  and r=2-sinθ

Q: Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of…

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 2+…

A: By sketching graph

Q: 6) Find the area of the region that lies inside the curve r = 3sin0 but outside the curve r = 2 -…

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Q: Find the total area of the region between the curves y = sin x and y = cos x for 0 &lt;=x&lt;=…

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Q: Find the area between the x-axis and the curve y = sqrt(1 + cos 4x), 0&lt;=x&lt;= pai

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Q: Find the length of the curve y = = cosh(x), 0 < x < 1. Arc length =

A: Arc length of a curve y=f(x) on [a,b] is given by, L=∫ab1+y'2dx ddxsinh(x)=cosh(x)…

Q: Find the area of the region enclosed between y = 3 sin(x) and y = 2 cos(x) from x = 0 tox = 0.5x.…

A:

Q: 2. Find the area of the region that lies inside both curves = 4 sin(0) and r = 4 cos(0) O +1 2T - 1…

A:

Q: 2. Find the area which is inside the first curve and outside the second. r = 4(1+sine) r= 4

A: Double integral is used to integrate function of two variable in two-dimensional region. If the…

Q: Find the area of the region which is in r = 3 cos(0) and outside the curve r = 2 – 1 cos(0)

A: The area is  43+8π3

Q: Find the area between y = 8 sin x and y = 10 cos x over the interval [0, π]. Sketch the curves if…

A: We have to find out the area bounded by the two given curves.

Q: the region bounded by the curves r = 2 cos 30 and x = y -1. %3D

A: Sol

Q: Find the area of the region enclosed by the curve a = 6 cos(t) – 3 sin(2t), y = 7 sin(t) with 0 <t <…

A:

Q: Use double integrals to find the area inside the curve  r = 3 + sin(θ).

A: Find the area enclosed by the curve r = 3+sin θ , using double integration method.

Q: Sketch the region enclosed by the given curves and solve for the area. y = 2 cos(4x),    y = 2…

A: The given two function are y = 2cos (4x) and y = 2sin (8x).The region enclosed by the curve y = 2cos…

Q: Find the area under the curve y= 1/(4x+ 2) for 1 ≤ x ≤ 3. Give an exact answer.

A:

Q: Find the area between y= 2 sin x and y = 5 cos x over the interval [0, 7]. Sketch the curves if i…

A: Given: y=2sinx y=5cosx

Q: Find the area inside the larger loop and outside the smaller loop of the curve + sin(0) 2

A: To find the area inside the larger loop and outside the smaller loop of the below curve. r=12+sinθ

Q: Find the exact area between a large loop and the enclosed small loop of the curve r = 1+ 2 cos Areas…

A:

Q: Find the area between the x-axis and the curve y = √1 + cos 4x, 0 ≤ x ≤ π.

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Q: Find the arc length of the curve y = ln(cos(x)) from x = 0 to x = 4

A:

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: Calculate the area of the region bounded by the graph of f(8) = cose sine and the 0 - axis %3!…

A: The given function is f(θ)=cosθsinθ. Simplify the function. f(θ)=2sinθcosθ2=sin2θ2 The function can…

Q: Find the area of the region bounded by the given pair of curves. Area inside the circle r = 3 cos 0…

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Q: Find the the region that lies inside the area OF Curve r- sin o and outside the curve r: 1+ sin 0.

A:

Q: r = 2 + sin 0, r= 3 sin 0

A: For given  r = 3sin(θ) r =2+sinθ Area is calculated as shown below

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.