1. The area of the region enclosed by the x-axis, the curve y = f(x) > 0, and the lines x = to f³(b) – 4f(b) for all b > 1. Find f'(1). b and x = b2 is equal

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

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Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: 13. Evaluate the given integral. ' x cost dt dx А. 2 В. О C. 1 D. x

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A: Given data  Used Simpsons 1/3 rule  f(x)=7e^(-πx)(sin(x^2)) With a=0 and b=2 and number of intervals…

Q: Using u = 1 + t°, the limits of integration will change from t = 0 to u = and from t = 1 to u =

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Q: 1. What should be A for the path independent of (2,4) 2Ay – x dy y? XY + A dx+ (1,2) Moreover…

A: Consider the given integral

Q: d) s x sin sin (4x²) d x X Sin X-y=- / 7xーy=17 てる。4) Set Up only Area bounded between the lines…

A: Ans A:

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

A: Answer is 7/12

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Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

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A: Note: As there is not any point as d. So we cannot solve question h.. Here is the solution of f…

Q: (a) Determine the appropriate Green's function by using the method of variation of parameters for…

A: Green's Function: The Green’s function approach is particularly better to solve boundary-value…

Q: 1. What should be A for the path independent of (2,4) xy + X -dx + 2Ay – x -dy. y? Y (1,2) Moreover…

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Q: 4. Find the exact values of each of the integrals below. f(x) (a) / f(æ) dæ (d) / F(2) dzæ 2 (b)…

A: We can see this function as f(x) = -x-5-4≤x≤-3-2-3≤x≤-22x+2-2≤x≤020≤x≤1x+11≤x≤2-3x+92≤x≤3-2x+63≤x≤4

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: The integral 1 = [(x* + 5e* + vx )dx is equal to:

A: Given integral is∫x4 + 5ex +x dxevaluate....

Q: 6. Suppose that w = x cos(yz²), where x = sin t, y = t² and z = 2e'. Find the rate of change of w…

A: Using derivative

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: 4. Supposea function y = f(x) is so be revokved at x = e from point (a, b) to (c, d), what is the…

A: Please refer the attached image for complete solution.

Q: The maximum rate of change of the function f(x,y,z) = x In(yz) at (1;2;) is equal to: V17/2 None of…

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Q: Suppose L is the tangent line of f (x) = csc T at x = 2 . Where does L intersect the y-axis? Note:…

A: We have to find

Q: x-3 dx r³+9x +9.x

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Q: Question 8 Set up an integral for the length of the curve yV1+x on 2 sxs3. x2 dx 9(1+x-)5/3 x2…

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Q: 1. Sketch the graph of the function y = f(x) = 3 – V4 – x² over [-2, 2] and use this to evaluate the…

A: Given: The function y=f(x)=3-4-x2,             Interval: [-2,2]             Integral:…

Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

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Q: 1.) Find the equation of the line tangent to f(x) = 6 ln(7– 3x)+5e-4 – 6x – 2 at x = 2 2.) Find the…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x 6 Sketch the region bounded by the…

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Q: 2. Given the joint pdf of X and Y, fxx(x, y) = { '0" (4xy 0<x< y <1 other wise Find the marginal…

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Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: 19. What is the derivative, of the function, dx dy y = 3x2 + 6x – 4 + 2e* – 3ln x А. dy 3 32x + 6 –…

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Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

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Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: 4-Évaluate the following integrals a) In dx b) ] ()"- dx 5/2 tan x

A: Integration:   The collection of all antiderivatives of f is called indefinite integral of f with…

Q: 1. What should be for the path independent of (2,4) 2Ay – x dp. y? xy + A dx + (1,2) Moreover…

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Q: 3. Apply Romberg quadrature to •1 1 dx 1+ x2 for h = 1, 1/2, 1/4, 1/8. Show a table of approximate…

A: We are given the following definite integral : ∫1/(1+x2) dx from 0 to 1 And we have to solve it…

Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: What is (V | and find the relative minimum dx point as indicated by the black dot on the graph at…

A: Here we have ;  y=xx ..................(1) taking log both of sides

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: 1. Find the average rate of change in y with respect to x over the interval [1, 7]. 2. Use the…

A: Given that: The function is f(x) = 4x -3 .

Q: Compute ∆y and dy for y =x + 5/ x − 1 where x = 3 and ∆x = dx = 0.1.

A: Consider the provided function, y=x+5x-1 Find the derivative of the function.…

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: s the indefinite integral | x2 cos(x3) dx becomes 1 cos(u) du- must also convert the integral…

A: Given query is to find the integral limits.

Q: Evaluate the integral. 10 r FIL √16 22 1 (x² + y²) 1/2 dy dx dz =

A: To evaluate the integral ∫04∫-44∫-16-x216-x21(x2+y2)12dydxdz

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: 4 16–x² Change the order of integration. Do Not Evaluate. 5tan xy dy dx

A: Answer

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.