Find the volume of the solid gen- erated by rotating the function - 14 f(x) = x(x – 10)(x + 3) - about the y-axis between the lines x = 1 and I = 4.

Q: Find the maximum and minimum values of the function f(x, y) = 3y² + 2x² – 6y %3D in the region where…

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Q: Given a cylindrical storage with 5m radius and 9m in height. If the radius is to increase by 0.1m…

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Q: Evaluate the integral. (Use C for the constant of integration.) t3 dt V1- t8

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Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Formula Used: Volume of the solid generated by the revolving the region bounded by the curve y=f(x)…

Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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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: Given that f (x, y) = 6x²y³ – cosx + 5y – siny + 10x, establish the fact that, the order in which…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A: The function fx,y=11-3x-y Then the taylor's formula for fx,y is, fxx,y=31-3x-y2fyx,y=11-3x-y2 Then…

Q: Find the absolute maximum and absolute minimum values of the function f(x, y) = x4 + y4 − 4xy on the…

A: Consider the equation

Q: 4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis…

A: Please check the region, given region is not bounded, we consider the region bounded by curve, x=0,…

Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: The integral. 1 dydx is VÆ V10 – y3

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Q: What is the isogonal trajectories cutting at angle of 0= arctan 4 to the family of curves whose…

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Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: The output at a certain factory is Q(x, y) = 6x² + 3e36. ỹ+ 3y. %3D where x and y denote,…

A: The function is Qx, y=6x2+3ex36y+3y2. The marginal rate of substitution is given by dydx=-QxQy…

Q: = x (with y > 0) about the y-axis can be computed using the method of disks or washers via an…

A: Given: Let us first plot the region.

Q: Use the second partial derivative to Find the relative extrema OF the Function f (x, y) = x°t…

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Q: Find the absolute maximum and absolute minimum values of the function f(x, y) 2x3 + 3xy + 2y %3D…

A: We have to find the absolute maximum and absolute minimum values of the function fx,y=2x3+3xy+2y3…

Q: Q5A) Find volume of body from above Z = √√4x² - y² and below Z - Triple integration. 1 using

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Q: Now integrate and simplify V = 2n x(100 – x²) dx. 10 10 v = 2n "(100 x t. dx 100x 2n 10 2 1000² = 27…

A: The given integral:V=2π∫010x100-x2dxWe need to integrate step by step.

Q: Q5A) Find volume of body from above Z=√√4-x² - y² and below Z = 1 using Triple integration.

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Q: Find the indicated higher partial derivative. a. f(x,y) = 3x5 + 2x³y² + 9xy*; fyxx a²c b. c = In (a…

A: As per our guidelines we are supposed to answer only three subpart of multiple subpart question.…

Q: Ca) f(x,y) = Jx² + y?

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Q: Given the function of two variables f(x,v) = In(/x7+y7). The partial derivative with respect to x is…

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Q: A cafe estimates a monthly profit (in thousand pesos) of P(x, y) = 27 – x² – y? + 6y if they open a…

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Q: S (x, y) sen (r2 – 0²) + In(r0 + 0), con Væ2 + y? A r = arctan

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Q: For the function f(x, y) = x4 + yA - 4xy on the set D = {I(x, y)| 0<x< 2, 0sys 3}, calculate the…

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Q: Find the elasticity of z with respect to y when y=2 if z = 10(x + 2)²+3)'. Enter the answer in the…

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Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: Evaluate the integral r4-x2 8x cos y dy dx r2 y – 4 by reversing the order of integration.

A: Evaluating the g8iven integral directly is not easy. So if we change the order of integration from…

Q: Find the real number a for which the value of the iterated integral V1- (y- (-2²- ỷ +2y) dx dy a-1 -…

A: Let fx,y=-x2-y2+2y. To determine the maximum value of the function, differentiate f(x,y) partially…

Q: Given that e2y, 10x2+4. f (x, y) = sin Enter a 10 significant figure approximation to the partial…

A: We will use matlab to find the answer

Q: Suppose f (x, y) = 2x2e?y. Find the partial elasticity of f with respect to y. Enter the answer in…

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Q: Find the partial integral. gy Y dx /1

A: y will behave as constant

Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: V = 200 /R volts in free space in the region bounded by 2mm <R <3mm, 0 <8 <n / 2 and 0 <o <n / 2…

A: Given 2 mm&lt;R&lt;3 mm, 0&lt;θ&lt;π2 and 0&lt;ϕ&lt;π2 Now, 2×10−3 m&lt;R&lt;3×10−3 m And under…

Q: The product of the triple integration w +y +z*)i dzdydx 9-2. استخدم الاحداثيات الكروية(

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Q: Find using the appropriate Chain Rule for W =y- 7x*y where x = e° and y = e", and evaluate the…

A: The given function is w=y3-7x2y where x=es and y=et. Differentiate the function w=y3-7x2y partially…

Q: S f(x.y)dxdy- Reverse the order of integration in 0,

A: The given integral is: To find the reverse order of integration.

Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: Find the partial integral. Y dy

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Q: Find the orthogonal trajectories of y = e where a be the arbitrary constant.

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Q: Q5A) Find volume of body from above Z = √√4 - x² - y2 and below Z = 1 using Triple integration.

A: I

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: Find the partial integral. 5y Y dx

A: Given, The partial integral ∫15yyxdx We have to evaluate the partial integral.

Q: Supply the missing integrand and limits of integration. 5 a) S S,2 6x²y dxdy = dy -5 сx/2 b) S S²…

A: We have to find the missing integrand and limits of given integration.

Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

Q: Find the absolute maximum and absolute minimum values of the function f(x,y)=x2+y3 on the region…

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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.