The probalitiy density unction of continous nandon vaniable x given below, Find c according ly- flx) = cx/2, -1Lx

Q: A college professor never finishes his lecture before the end of the hour and always finishes his…

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Q: of f(x) = x +1, g(x) = e-, the vertical line r =-1 and the region R be %3D these curves. f -2 1 If…

A: We are authorised to solve only one question please repost remaining questions  Volume of revolution…

Q: he region bounded by the curve = sin y- cos y 4 for 5л sys evolves about the y-axis 4 ee diagram).…

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Q: 2) Find an integral that equals the moment about the z- y = ; 0< < 1, if the density (mass per unit…

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Q: Assuming that z is a differentiable function of x and y, Let F(x,y.2) = In(x*y) – e" - tan Find F.…

A: Here, the given function is: F(x,y,z)=ln(x2y)-eyz-tan-1z...(1) where z is a differentiable function…

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Q: 5.25. Find (a) the area and (b) the moment of inertia about the y axis of the region in the xy plane…

A: a first we will find the area bounded by the y=4-x2 and the x-axis Intersection points between the…

Q: Let f (x) = COS X sin x for 0 0 and where is f (x) < 0?) A =

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Q: 1. Let the joint pdf of X and Y be given by fxy(r, y) = C exp + ry where C > 0 is an unknown…

A: Please note that as per our guidelines we can answer only the first three sub parts. Please post the…

Q: Let X and Y have the joint density function Kry 2<1<4 and 4< y56 fxy(x,y) = otherwise i. Find K so…

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Q: The joint pdf is given as fxy(x, y) = Ae (2x+y) for x ≥0 and y ≥ 0 Find (a) the value of A and (b)…

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Q: Determine the volume of the solid generated when the =1/2 area bounded by y = sin I: X-axis ; x =0…

A: In this we have to find the volume generated by revolution of a curve.

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A: Here is the solution of the given problem. Moment about x-axis.

Q: 11 The linear density p in a rod 3 m long is kg/m, where x is measured in meters from one end of the…

A: We know that: fave = (1/(b-a))*Integration of function with lower limit 'a' and upper limit 'b'.…

Q: 5.05* Consider a rv X with density function f(x) (a) Evaluate k. (b) Obtain the corresponding cdf…

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Q: The weekly demand X for kerosene at a certain supply station has a density function given by [x for…

A: a) P12≤X≤32=P12≤X≤1+P1≤X≤32=∫121xdx+∫13212dx=x22121+12x132=122-1222+1232-12(1)=58

Q: A college professor never finishes his lecture before the end of the hour and always finishes his…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: 2.) Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic…

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Q: (a) Find the marginal density function for Y,. f2(Y2) = , where (b) For what values of y, is the…

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Q: c. Find the area of the reqion bounded by y xe-a and the x-axis on the interval 0,bl. Because this…

A: Given curve is The area of the region bound by the curve and x-axis on the interval [0,b] is given…

Q: 2. 3. 4 4. 16 Use Simpson's rule to estimate (i) the area enclosed between the curve, the x axis and…

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Q: A region R is bounded by the graphs of y3D0.1 x and y=0.1x. Find the moments M, and M, of R about…

A: The moment of region R is given by, Mx=∫∫ydydxMy=∫∫xdydx From the given region, y varies from y=0.1x…

Q: Find the average value of f over region D. f(x, y) = 3x sin(y), D is enclosed by the curves y = 0, y…

A: Here, the domain D is the area enclosed by the curves y=0, y=x2 &amp; x=7 is: A=∫07∫0x2dy…

Q: If m s f(x) s M for a s xs b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: The table of values represents a function f(x). Using the trapezoidal rule n=4 subintervals,…

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Q: = Find the area A of the region that is bounded between the curve f(x) = ln (x) + 1 and the line…

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Q: A solid S is generated by revolving the region between the x-axis and the curve y =√ sinx (0 ≤ x ≤…

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Q: O 2.) Let X denote the diameter of an armored electric cable and Y denote the diameter of the…

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Q: 1. Find the density of Y = 1- e-ax when X ~ Exp(X). Note that the density of X is if r > 0, ,…

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Q: Consider the graph shown in the figure, which gives the velocity of an object moving along a line.…

A: Consider the given velocity to time graph, a. the area under the velocity-time graph represents the…

Q: h. For any continuous function f on [a,b], the solid formed by revolvingfabout the x-axis has at…

A: The volume of solid that is obtained by the revolution of a function can be evaluated by using…

Q: A college professor never finishes his lecture before the end of the hour and always finishes his…

A: For the given problem ( b)p( within 1 min ) =? ( c ) p( between 30 and 60 sec ) =? ( d ) p( atleast…

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Q: upposed to be filled to a pressure of 40 pounds per quare inch (psi). Let X denote the actual air…

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Q: A region R is bounded by the graphs of y=0.1 Vx and y=0.1x. Find the moments My and My of R about…

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Q: Find the area of the region enclosed by y = 4.25x and r = 6.5 – y?. 3 Use horizontal strips to find…

A: The region is enclosed by the curve y=4.25x and x=6.5-y2.

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Q: Let R be a region bounded by x- axis, the curve y= cosx between x= -lines. If the region Ris…

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Q: R is the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=1 and x=4.…

A: Given: 1) The given region is bounded by y=x4+x, y=0,x=0 and x=2 about the line x=4 2) The given…

Q: find the volume of revolution about the x-axis for the given function and interval. f (x)= 2/x + 1,…

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Q: rve Y= x (x+5)(x-3) between the va rea of the finite region bounded by ven quantity in terms of sin…

A: We have to find the following given conditions according to the given information

Q: Let T and T, represent the lifetimes in hours of two linked components in an clectronic device. The…

A: Given: T1 and T2 are the lifetime in hours of two linked components in an electronic device. Region…

Q: Left f(x) = x? + 3. Approximate the area bounded by the curve y = f(x), the x-axis, and the vertical…

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Q: Assuming that z is a differentiable function of x and y, Let F(x,y.2) = In(x?y) – e" - tan-1z. Find…

A: topic - partial derivative of a function

Q: In which region on ry-plane the function f(x.y)=In(x+y) is not continuous? A. except r = 0 B. except…

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

Q: ith uniform density (mass/unit length) 6(z) =5+ sin(z) lies on the z-axis between z = 0 a

A: Introduction: The formula of the total mass of a rod with density function δ(x) with a≤x≤b is given…

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Q: The length of time Y , in minutes, required to generate a human reflex to tear gas has the density…

A: From the given density function of Y, we need to find Standard deviation of Y.

Q: C. Set-up the definite integral to find the length of the arc of the graph of y = Vx-1 from x = 2 to…

A: (C) Given the curve is y=x-1 and x=2,x=5. Find the arc length of the curve y=x-1 from x=2  to  x=5.…

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.