Use the surface area formula SA = /I. V1 + f% + f; dA to prove that the surface area of the sphere of radius p> 0 is SA= 4#p².

Q: Find the area bounded by the indicated curves. x=2y2 – 1, x= y? +8 109 OA. 3 О В. 36 ОС. 24 O D. 27

A: We will sketch the graphs and find the points of intersection. Then we will mark the appropriate…

Q: 2y? and x = 4 + y²

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Q: Find the surface area of the cylinders below. r= 0.8 in. h = 2 in. 1. r= h= S= 2nr? + 2nrh S= 2*n*(…

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Q: Find the equation to solve the surface area obtained by revolving the parabola x? = 4y from x = -2…

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Q: HW: Find the area of the surfoce generaled by revolving 1. x= Vy,1sy s8 about the x- axis.

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Q: Find the area between the curve x = 2r*, y = 31 +1 and the x-axis, 0<t<2 !!

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Q: 22. Find the area enclosed by the curve r²-4coss. c. 16 B. 8 D. 2

A: Given equation of the curve is r2=4cosθ. We know that, area under the curve is given by A=∬Rrdθdr.

Q: Find the area enclosed by the curve 5y? = 16x and y² = 8x – 24. Answer: sq. u.

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Select the formula for the Volume of the cone 2. T:r·h+ 2·T• r2 1 T• p2 . h 3 O2. T. r2 . h T:r·h² +…

A: The volume of a cone of radius 'r' and vertical height 'h' is given by the formula     Volume of…

Q: Use the Surface Area formula to find the Surface Area of each Rotated figure along the given…

A: The definition of surface area is the total area of the surface of any 3 dimensional object that are…

Q: Find the surface area generated by rotating the parabola arc y = x² about the x-axis from x = 0 to x…

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Q: Find the z-score that best satisfies the condition. 10% of the total area is to the left of z. z=?

A: It is required to find the z-score, that separates the bottom 10% of the area and the rest of the…

Q: Find the area of the regi on. X = 4¢3- t2 y= t* + 2t?

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Q: Find the areas enclosed by the following curves: (c) y = xv1 – x², and y = 0 |

A: The area enclosed by the curves y=x1-x2, y=0. So, area enclosed by the region is: A1=∫-10∫0x1-x2dy…

Q: Q3: Find the volume of the solid enclosed by the parabola y = x? + 22 and the coney = 32 — x? — z2,

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Q: Find the real number b such that the volume of solid B (r, +

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Q: Find the surface area of the figure when d = 8 cm. For calculations involving x, give both the exact…

A: We have to find the surface area of sphere Using formula surface area 4πr^2

Q: Sketch the graph and set up the integral of the area of: a). Inside r1, but outside r2 b). Inside…

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Q: Describe a region whose volume is equal to: (а) 27 | p² sin o dp dộ dô Jo (b) /4 2 rdr de dz -2 J7/3…

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Q: What is the area of a sector ACB? Leave your answer in terms of T. 108° 5ft

A: Solution of this question is

Q: ind the volume of the solid generated by revolving the region in the first quadrant bounded by the…

A: Given problem:- Find the volume of the solid generated by revolving the region in the first quadrant…

Q: Find the area of the surface obtained by revolving the curve y=2/4=x, for 1<«<4, around the x-axis.…

A: Explanation of the solution is given below...

Q: Q3: Find the volume of the solid enclosed by the parabola y = x² +z? and the cone y = 32 – x² - z2.

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Q: Find the approximate area under the curve of f (x) =x+1 from x = 0 to x = 2, using 4 left-endpoint…

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Q: The area which is enclosed by the curve x2 – 10x + 4y + y? = 196 is O 12n 15n О 14п 144n O 225n

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Q: Show that the volume common to the surfaces 2 p2+z=4ax and x+y?=2ax is (3r+8)*. 3

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Q: Find the area enclosed by the given curves. 10) y = - 4sin x, y = sin 2x, 0 < x < n B) A) 16 C) 8 D)…

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Q: Find the area enclosed by the given curves. y = x°, y = 4x 4. O 16 2 8.

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Q: Find the area enclosed by the loop of the curve x = t3 – 3t, y = t² +t+ 1.

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Q: 2) Find the area enclosed by the curve a =t² – 2t, y = vt and the y-axis.

A: To find the area enclosed by the curve x=t2-2t,y=t and y-axis. For that, first, find the point where…

Q: By sketching the graph and using integration, find the area of the region bounded by the ellipse and…

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Q: Find the area inside both curves: r = 3+ 2sine and r = 2

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Q: Find the area of the shaded region. y= sec?x V- cos x (B c) 1. D 2. 2

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Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

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Q: Find the area of the shaded region 14 LA bounded above by y = 2, bounded b TE lo 1)

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Q: nd the volume of the solid that results when the region enclosed by 0, x = 7, and y = 0 is revolved…

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Q: For what values of m do the line y=mx and the curve y =x/(x2+1)enclose a region? Find the area of…

A: The given  line is y=mx    ...1. The given  line is y=xx2+1    ...2.

Q: Find the area enclosed by the x-axis and the curve x = 1 + e t , y =t-t2.

A: find explanation below

Q: Find the volume of the solid formed by revolving f(x) = (x + 2)/2 about the x-axis on the interval…

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Q: What is the area bounded by the curve defined by the equation x2 = 8y and its latus rectum? %3D а.…

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Q: The area enclosed by the curve r = 3cos3e is *

A: Here, we need to find the area enclosed by the curve r=3cos(3θ)

Q: Q1 Answer with all details, By y = sin x Using Two method, find the area of shaded region in beside…

A: Area under curve

Q: Q6 Determine the surface area of the solid obtained by rotating y = V(2p – x)(2p + x), |x | < 2…

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Q: The formula of calculating the surface area with equation z = f (x, y), where and are Ôx ôy…

A: Here, z=x2+y2and the given cylinder is,x2+y2=2x

Q: find the area of the cylinder z=x+y2 that lies below the second-quadrant area bounded by x axis,…

A: Given that: find the area of the cylinder z=x+y2 that lies below the second-quadrant area bounded by…

Q: By rotating the line y = r about the x-axis, for x in the interval [0, h], and applying the surface…

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Q: Find the real number b such that the volume of solid B = (r, y, z) | a² + y² + z2 < Pand 0 2 5 be…

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Q: Find the area bounded by the curves y = 4 Vx and y 4х 3 а) -18 b) 09 c) -9 d) O18 e) 036

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Q: For what values of m do the line y =mx  and the curve y= x/(x2 + 1)enclose a region? Find the area…

A: The given line is y=mx and the curve y=xx2+1. The given line and the curve will enclose a region…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 51 and the upper cone z? = 3x2…

A: Calculus Question

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.