Problem 4  The volume of the solid obtained by rotating the region enclosed by y=1/(x^3), y=0, x=2, x=7  about the y-axis can be computed using the method of cylindrical shells via an integral  V=∫___________ dx (with lower limit a and upper limit b)  with limits of integration a=_________ and b=__________ the volume is V= _______________ cubic units

Q: 2 Solve S dy Use u substibation with u=y² ¢ CLearLy show gamma function r (n+2) = nTn) propeaties

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Q: 20. y dx = (x + vy² – x²) dy. arc sin (x/y) = In |y/cl. ANS.

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Q: 05: Methane - air represent diffusion flame, if the mixture fraction governing equation d²z dz is…

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Q: Question 3 Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the…

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Q: The indicated functions are known linearly independent solutions of the associated homogeneous…

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Q: Problem 12  The volume of the solid obtained by rotating the region enclosed by  x=3y, y^3= x (with…

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Q: Problem 12 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=5x   about…

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Q: Problem: Evaluate the double integral: (y – 12z) dz dy |

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Q: Problem #1: Use cylindrical coordinates to find the volume of the solid bounded by the graphs of z -…

A: Given, z=70-x2-y2z=6 We have to calculate the volume of the region E by using the cylindrical co…

Q: The equation of motion of a particle moving from rest, towards a center of attraction point, d²ß ds2…

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Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: 5. Find fSp(x + y)² dx dy, wh- region in Fig. 17.2.12. y = x

A: Answer is 7/12

Q: Problem 8  The volume of the solid obtained by rotating the region enclosed by y=(x^2), x=2, x=3,…

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Q: Problem 7 The volume of the solid obtained by rotating the region enclosed by  y=1/(x^5), y=0, x=1,…

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Q: 8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y…

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: ion 8 apply General Power Formula of Integration on which of the following sinhucothudu cosha coshu…

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

Q: Solve intial value problem to: y"+2y'+4y=e^(5t)+(sin^2)t; y(0)=1,y'(0)=1

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Q: Problem 8  The volume of the solid obtained by rotating the region enclosed by y=(e^3x)+3, y=0, x=0,…

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Q: Convert the double integral into a type II double integral

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Q: A pilot is told by ground-control that he will encounter unusual air flow streamlines in his flight…

A: Here we will show the required result.

Q: evaluate by using polar coordinates. Sketch the region of integration first.

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Q: 35. { (р, ф, 0): 1 <p< 3}

A: Given:The spherical coordinates are being set as

Q: and y) - what is the inital va lue solution of the probem a) aresin x 61 y= arc'sinx + 211/3 y= arc…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 4. x2 (In x - In у) dy 3D у (ylny— ylпx) dx

A: Solution

Q: Problem 11 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=4x, about…

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Q: y Problem 4: Find the centroid of the shaded area between the curves by integration. Y1 = cosx Y2 =…

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Q: sin(2a)dx + cos (3y)dy 3 0, у(т/2) — п/3 ||

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Q: Work Problem 1 a) Sketch the region of integration and evaluate the double integral b) Change the…

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Q: Problem 3 The volume of the solid obtained by rotating the region enclosed by y=21x-(7x^2), y=0…

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Q: (b) Given the second order boundary value problem y" +4y= sinx, y(0) = 0, y(1) = 0. (i) By taking…

A: Given differential equation is y'' +4y =sinx,    y0=0,  y1=0   Part (i):- step size h =0.25

Q: 2) [(1+ x) 0 < x < 1 = 0, u(0) — 0, и(1) %3D1 dx dx Find the variational form of the boundary value…

A: Given,

Q: If exact solve If not use an integrating factor. Also, If an inidal condition is given, find the…

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Q: particular solution of the equation for the given boundary condition. (x2 + sin y)dx + (x cos…

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Q: A pilot is told by ground-control that he will encounter unusual air flow streamlines in his flight…

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Q: Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about…

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Q: Consider the Boundary Value problem a²u + = 0, 0 < x, y < 8 dy? и(х,0) — а(8 — г), и(п,8) — 0, 0<а<8…

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Q: Problem 13  The volume of the solid obtained by rotating the region bounded by x=(y^2), x=5y  about…

A: Sketch the region using a graphing calculator The shaded region is rotating about the y=5 line

Q: Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about…

A: y=(x^2), y=3x  about the line y=9

Q: a²p Using the partial differential equation goveming of + = 0, detemine the pressure distribution of…

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Q: Problem 10  The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=2x, about…

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Q: Problem 4. The bell-shaped curve y = f(x) below satisfies dx = -xy. R y= f(x) a (a) Use cylindrical…

A: Consider the provided question, (a) We have to show that the volume, V=2π1-c where c=f(a) First find…

Q: 1. Find the area bounded by the curve x2 -8+y=0 and the line 2x=y

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Q: Problem 8. Using Euler's Method (h = dx = 0.02, xn = 0.1), find y(xn) for the boundary value problem…

A: Given y′=x2-y2 y(0)=0 h=0.02 y(0.1)=?Euler…

Q: Problem 9  The volume of the solid obtained by rotating the region bounded by x=(9y^2), y=1, x=0…

A: Sketch the region using a graphing calculator Shaded region is rotating about the y axis.

Q: 9 1 [y sin x dx dy 0 0 What do we get if we write the integral with the variable equation = Vỹ , v=…

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Q: 01 (test for exactness) * 4 points (siny - ysinx) dx +(cosx +xcosy) dy =0 01 (solve exact de) * 4…

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Q: Problem #5: Find the volume of the solid bounded by the graphs of r = 4 sin 30, z = 5+ Vx² +y2, z =…

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Q: Problem 19.4. (1) Compute the volume Vi of the solid obtained by revolution of the region between…

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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.