1 TIy. Suppose that the The volume of a right circular cone of radius x and height y is given by V = dy when x = 5 and y = 9. dx volume of the cone is 757 cm³. Find dy dx

Q: Evaluate the double integral : (y – 10x) dx | dy

A: we will integrate first inside the bracket with respect to x taking y as constant and then we will…

Q: For the integral 3xe"c fute - w - ftu °dx, we can use integration-by-parts: UV – First, if we let dv…

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Q: Find a formula for the integral. dy = y 3(1– 6y) Incorrect

A: We have ∫e6xe3ydy

Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

Q: 2. Use Euler's method to find the approximate value of y correct up to 4 dy decimal places for…

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Q: plutions of (e + In y +2) dx + ( + In z + sin y ) dy

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

Q: 1 The volume of a right circular cone of radius r and height y is given by V = T2*y. Suppose that…

A: use implicit  differenetiation to find the unknown.

Q: Find dy. y=3 In (4+x) dy =D

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Q: If the curve y = ln x between x = 1 and x = e is rotated about the y-axis, which integral below…

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Q: The volume of a right circular cone of radius x and height y is given by V = volume of the cone is…

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Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

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Q: Integrate the given item by changing the order of the integral. * dx dy 1).

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Q: 1 The volume of a right circular cone of radius a and height y is given by V = ²y. 3 when x = 6 and…

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Q: Evaluate the multiple integral.* 22y [ ✓²)¢ dx dy 10 17.5 16.5 The area hounded by the graphs of y=

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Q: Evaluate the double integral : (y – 8x) dæ| dy

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Q: Evaluate the double integral : (y° – 10x) dx| dy

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Q: The volume of a sphere is expanding wherer = 2t. What is the rate of change in volume with respect…

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

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,…

Q: ) Find the area of the surface that is obtained by rotating the curve Y = 0.25X² – 0.5 Log.X, 1<X<2…

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Q: dy For = 2x +y and y(0) = 2, use Euler's method with h=0.1 to approximate y(0.5). dx Approximating…

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Q: Figure out these antiderivatives. S dx /1-х2 arctan(x) dx 1+x? ( In(x))* dx 2x

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Q: Show that the antiderivatives are equivalent.                                                     ∫…

A: To show that ∫3x21-x6dx = arc sin x3+C Substitute  u = x3. Then                  dudx=3x2du  =3x2dx…

Q: Evaluate the triple integral ∫ 2 to 0 ∫ 2x to 0   ∫ ln x to 0 xe^−y dy dx dz

A: The given integral can be written as: I=∫20∫2x0∫lnx0xe-ydydxdz…

Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y. How is dV/dt…

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Q: 1 cone of radius x and height y is given by V = =Tx2 y. Suppose that the 3 dy Find when x = 2 and y…

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Q: In x The triple integral ye² dz dx dy is equal to the triple Y a ln x integral ye dx dz dy.

A: The given statement is: The triple integral  ∫12∫yy2∫0ln x yez dz dx dy  is equal to the triple…

Q: Use the Trapezoidal Rule with n = 6 to ex approximate dx | 1 х Use the Simpson's Rule with n = 6 to…

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: Differential

Q: e following integral: 23 8xyz dz dx dy. 120

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Q: . If y = Arctan sinh e then dy/dx is A. e sech e C. e sinh ex B. e* csch e D. e cosh e

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Q: 1 The volume of a right circular cone of radius x and height y is given by V = Txʻy. Suppose that…

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Q: Evalúe la integral doble. ln xy dA,D está acotada por x = = 0, x = V1- y? %3D |

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Q: Evaluate the iterated integral. 8 1 (3х — 9у) dy dx - Exact number, no tolerance. 8 (Зх — 9у) dy dx…

A: Given:      ∫18∫-113x-9ydydx     =∫18∫-113x-9ydydx integrate with respect to y…

Q: 5. Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

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Q: Evaluate the iterated integral. (2х — 4у) dy dx Exact number, no tolerance. (2x – 4y) dy dx = i -1

A: The given integral is: I=∫111∫-11(2x-4y) dy dx

Q: plest iterate integral. 36 – x2 ,36 х dz dy dx 36 – x2°x2 + y2' dz dr de dp dφ de

A: Given that ∫-66∫-36-x236-x2∫x2+y236xdzdydx Take x2+y2=r2 Where x=rcosθ,y=rsinθ So, the integral…

Q: 2 -πx²y. = The volume of a right circular cone of radius ï and height y is given by V 3 dy when x 4…

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Q: E valuate dt + seck tan x dX

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Q: Which of the following integrals represents the length of the curve y = 2", 0<x < 3? 3 А. 1+ 22x dx…

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Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: S dx dy dz 1 Evaluate the triple integral 1 xyz

A: Given that, the integral ∫1e∫1e2∫1e3 1xyz dx dy dz To evaluate this triple integral

Q: Evalate The following Impreper integrols ロS dx I+ X2 eや。 2 え 3] X2 Jx (X-リ% dx (Xーリ(メー4)

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Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: 1 The volume of a right circular cone of radius x and height y is given by V Tx y. Suppose that the…

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Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

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Q: 1 The volume of a right circular cone of radius x and height y is given by V TXʻY. Suppose that the…

A: Given that:                        Volume of the cone, V=13πx2yV=204π cm3x=6y=17

Q: Can you help me step by step?

A: Let u=1+x^4

Q: Evaluate the iterated integral. (8x – 8y) dy dx Exact number, no tolerance. (8x – 8y) dy dx = i %3D

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

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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.