Q2/ Let the curve (r = sin e + cos e) 1. Identify the symmetry of the curve. Then sketch the curve in xy-plane. 2. Find the area of the curve region.

Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: Find the length of the curve. The cardioid r= 3(1- sin 0)

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Q: Find the area of the surface obtained by rotating the curve from x = = 0 to x 5 about the y-axis. =…

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Q: Q.8 Find the area of the surface generated by revolving the curve x = 9-y. (-25ys2) about the…

A: The solution are next step

Q: The region bounded by the curves y = r² and y = x³ is rotated around a. the z-axis; b. the y-axis;…

A: the region bounded by the curves y=x2 and y=x3 is rotated around  a) the x-axis b) the y-axis c) the…

Q: a. Arc length of the curve y = 4- (x-2)² 4 bordering the region R

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Q: Where do the curves of y cos(x) and y = x³ - 1 = intersect? Use bisection.

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Q: Q5/ Calculate the Arc length of the curve (y-1)° = x x= (y – 1)*2 , 1<y25 (don't need to draw).

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Q: Find the arc length of the curve r 2sin () from 0 0 to 0 = 7.

A: To find the arclength of the polar curve.

Q: y = 4x3 from x = 0 to x = 6 about the x-axis. The area is

A: The curve given is  y=4x3 The interval is [0, 6]

Q: Q2) Find the area of the surface generated by revolving the curve y=√4-x² about y-axis.

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Q: Find the area of the surface generated by revolving the given curve about the y- axis. x = /25 - y²,…

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Q: Find the area enclosed by the given parametric curve. (Use a calculator to look at the graph.) y =…

A: given

Q: 1/B) Find the length of the cardioid 'curve: r = 1 + cose

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Q: Find the area of the surface generated by revolving the curve y = Osxs2, about the x-axis. 392x The…

A: We have to find the area of surface.

Q: Sketch the region enclosed by the given curves. y = 2 cos(6x),    y = 2 − 2 cos(6x),    0 ≤ x ≤ π/6

A: Find the intersection points:

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 5 about the x-axis.…

A: It is given that the curve y=2x is rotated from x=0 to x=5 about the x-axis. The objective is to…

Q: Find the area of the surface generated when the indicated arc is revolved about y-axis. X^2 = 4ay…

A: If the continuous curve is described by the function y = f(x), a ≤ x ≤ b, then the integral becomes…

Q: Find the area of the region enclosed by the inner loop of the curve. r = 6 + 12 sin(0)

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Q: Find the length of the curve The cardioid r = 1 + cos u

A: Solution:Given             r=1+cos uFormula:l=∫θ1θ2r2+drdθ2dθ

Q: Find the length of the curve y = cosh(x), 0 < x < 1. Arc length : %3D

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Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², -1s×<1 about the x-axis is

A: As per the company's guidelines, we are supposed to solve first question for you,  kindly repost the…

Q: Find the area of the surface obtained by rotating the curve about the y-axis. = (y² - Iny), 1 ≤ y ≤…

A: surface area  about  y axis  bounded by  x=g(y)Area=∫ab 2π g(y)1+g'(y)2  dy

Q: 8.) Find the area of the surface by revolving the curve about each given axis. 1 x =t3, y = t + 1,…

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Q: Find the area of the surface generated by revolving the given curve about the y- axis. x=2₁√√6-y,…

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Q: Find the area enclosed between the parametric curves x=2t^2 + 6 y=e^-5t and x-axis for t greater…

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Q: Write an integral that represents the arc length of the curve on the given interval. Do not evaluate…

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Q: Find the area of the surface obtained by rotating the curve y 5æ? about the y axis for 3 < x < 8 -…

A: Given: y=5x2

Q: A thin plate of constant density d = 1 occupies the region enclosed by the curve y = 36/(2x + 3) and…

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Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

Q: Find the area of the region that lies inside the curve r = 1 − cos theta and outside the curve r =…

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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 <…

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Q: Sketch the curve. r=3-sin(0) 1 Find the area that it encloses. 1 2 3 2 + -2 1 2 -2 -1 1 OO 3 -3 -2 2…

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Q: Find the area of the surface obtained by rotating the curve y = sin(4x) about the a- axis from x 0…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 5 sxS 21

A: The equation of the given curve is y=13x32.The curve is bounded between x=5 to x=21.We have to find…

Q: 2. the area of the curve r-a cos 2 0

A: The curve contains two petals,

Q: Find the area of the surface obtained by rotating the curve about the x-axis. Recall: S=2n |…

A: Find the surface area

Q: Find the area of the surface obtained by rotating the curve y = V6x from x = 0 to x = 2 about the…

A:

Q: Find the length of the curve. The cardioid r = 7(1 + sin 0)

A: Given: The arc length of the cardioid is calculated by using the following formula,

Q: Sela'y-J) dy. Cis the arc of the curve y- Vx from (1. 1) to (4, 2)

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: The region enclosed by the curve r= 4 cos e

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Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: Find the area of the surface obtained by rotating the curve y = 3x3 from x = 0 to x : 4 about the…

A:

Q: Find the area of the surface obtained by rotating the curve y=4x3 from x=0 to x=2 about the x-axis.…

A: The curve isy=4x3 So, its derivative will be: dydx=12x2 As,  Sx=∫2πy dswhere ds=1+dydx2dx so,…

Q: Y=Ğ jfor exS3; about The X-axi's

A: The formula for the surface area generated by rotating the curve  A=2π∫abf(x)a+(f'(x))2dxHere…

Q: Sketch the region enclosed by the given curves. y = 4 cos(pix), y = 8x2 − 2

A: The region enclosed by the curves y=4 cos πx and y=8x2-2

Q: Find the area of the surface generated by revolving the given curve about the y-axis. x = 8y + 3, 0…

A: Note: If x=fy≥0 and continuously differentiable on a,bThe area of the surface generated by revolving…

Q: The curve y = V4-x², -1<x<1, is an arc of the circle x2 + y² = 4. Find the area of the surface…

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Q: for the Surface Area below.. what is the * ?radius of revolution Q3/ The arc of the curve x-Vy, from…

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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.