QI: For: ffdA a) Write the adequate orders of the integral formed by the common region y=1-x, y =1-x;0SIS1? b) Write the area using single integral? c) The area is equal :

Q: Find 5 dA over the region R = {(r, y) | 0 < x < 5,0 < y < 4} by identifying it as the volume of R a…

A: Given,  ∬R5 dA, R={(x,y)|0≤x≤5,0≤y≤4}

Q: Set up triple integrals for the volume of the sphere p=11 in a. spherical, b. cylindrical, and c.…

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Q: Evaluate the triple integral R. where R is the region enclosed by the sphere r2 + y² + 2? = 9.

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Find the area of the region R: 0&lt;= x&lt;= 2, 2 - x&lt;= y&lt;= 24 - x2, using (a) Fubini’s…

A: First, find the area of the region by Fubini’s theorem:

Q: The integral Sr Si rdz dr do represents the volume of a solid. What is the solid? half a cylinder…

A: Cylindrical coordinates :       x = r cosθ , y = r sin(θ) , z=z where,    x2+y2 = r2   and θ =…

Q: Find the area, A, of the region enclosed by the cardioid r = 8+8 cos 0. (А) 96 я (В) 48 я с) 52 я…

A: The area enclosed by the cardioid r=8+8cos θ is given by: A=12∫02πr2dθ=12∫02π(8+8cos θ)2dθ…

Q: Let R be the annular region Tying between the two circles x + y- x? + y? = 5. Evaluate the integral…

A: The solution follows as :

Q: In Exercises 31–50, sketch the region enclosed by the curves and compute its area as an integral…

A: Note: As per our company guidelines, we are supposed to answer only one question. Kindly post the…

Q: Consider a region R, which lies above the x-axis and between the circles x? + y? = m² and x? + y =…

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Q: Use a triple integral to find the volume of the solid shown in the fig z = 64 – x² – y? 20 60 50 40…

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Q: 2. Find the volume of the region enclosed by two spheres S =2 +y°+? =1, S = 2² + y² +(z-2)² = 4. %3D…

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Q: f(x, y) = xy, R = {(x, y): x² + y² < 16}

A: Polar coordinate and rectangular co-ordinate  x=r cosθy=r sinθx2+y2=r2θ=tan-1yx The integral will be…

Q: Q3-Find the volume common by the plane x+y=a? & x*+z=a? ?

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Q: Find the area of the region bounded by 0 = ,0 = , and r = csc e. %3D %3D 3

A: As per answering guideline, we can answer to first question. Please repost the other question. Thank…

Q: Evaluate the double integral dA, over the rectangular R Vx² + y? + 1 region R = {(x, y) : 0 < x < 1,…

A: Given: ∫∫Rxyx2+y2+1dA R=x,y:0≤x≤1, 0≤y≤1

Q: Q: Sketch and find the area between y = x2 and y = Vx, || using double integral. ( find ſſ dxdy , ſ…

A: As we know that we can find the area between 2-curves by double integration. Area=∫ab∫g(x)f(x)dydx

Q: Consider the integral a* – y´ dA where Ris the region in the second quadrant bounded e between the…

A:

Q: Evaluate by two methods the integral || ydA, where D is the region bounded by the line r - y = 0 and…

A: compare two equations (x,y) = (-1,-1) (x,y) = (2,2) from second parabola equation x = -2  then y = 0…

Q: 2. Set-up the integral for the area A(R) of the region R bounded by the circles y? +x? = 1, and y? +…

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Q: Sketch and find the area between y = x² and y = Vx, %3D using double integral. ( find ſf dxdy , f…

A:

Q: (a) Set up an integral for the volume of a solid torus (thedonut-shaped solid shown in the figure)…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Each integral represents the volume of a solid.Describe the solid 2 pie [integral 0 to 2          (…

A:

Q: The density of a plate is given as p (x, y) = x + 2y g/ cm?. Find the mass of the plate by…

A: Let x=r cos θ      y=r sin θGiven: R is the region below the line y=x and is bounded by the circle…

Q: 2 = 5, 2 = v2x2 + 2y2 1 - Calculate the volume of the area (using the triple integral

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Q: Find the volume of the region enclosed by z = 1 – y? and z = y? – 1 for 0 < x < 60. V =

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

Q: Use integration to show that the volume of the closed unit ball B = {(x,y, z) : x? + y? + z2 < 1} in…

A: As per Bartleby guidelines, for more than one question is asked only one is to be answered. Please…

Q: y = 9(x) y = f(x) 1 A B x Aa C

A:

Q: Find the volume of the solid generated if the area bounded by y = x² and y = x5 is rotated by the…

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Q: What is the area of the greern region. B as an integral? o ) dr 1 9 (z) dz of) dz + 1(1) dz What is…

A:

Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

A: We have to find the volume by using triple integral

Q: Determine the volume generated of the area bounded by y=√√x and y=- (A 128/15 (B) 112/15 Ⓒ136/15 (D…

A:

Q: Use Gaussian quadrature with two Gauss points to evaluate the integral over the area A in the graph.…

A: Answer is mentioned below

Q: Find 6dA over the region R = {(x, y) | 0 < x < 3,0 < volume of a solid

A: In this question we will use basic of calculus i.e concept of application of integration. We will…

Q: Evaluate the double integral /VA- y? dA, R where R is the region bounded by the circle x² + y? =

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Q: Find the area of region enclosed by x = t – t, y = t – tº, 0 < t < 1 using Green's Theorem.

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Q: Which integral should be used to calculate the volume of the solid cube with side lengths all 17…

A: Cube with all sides 1. Let's assume a small cube with dimensions dx, dy, dz in the given cube.…

Q: Calculate the area of the region R bounded by (ANSWER IN DECIMALS) y = 0, y = 2, y = 2 – (x + 2)“, y…

A:

Q: 5. Use a triple integral to find the volume Of the gNen solid The terrahcdron enclosed by the…

A:

Q: Each integral represents the volume of a solid.Describe the solid.  pie integral 2 to 5 y dy

A: Consider the given integral that represents the volume of a solid π∫25ydy

Q: In the formula y -| A(u)đu used to compute the volume of a solid: a

A: Given,          In the formula V=∫abAudu used to compute the volume of a solid.

Q: Sketch the region enclosed by ?=5?y=5x and ?=3?2y=3x2. Decide whether to integrate with respect to…

A: Given: y=5x, y=3x^2

Q: Compute the volume lying inside the sphere x? + y? + z? = 37 but outside of x² + y? = 21.

A:

Q: Q: Sketch and find the area between y = x2 and y = Vx, %3D using double integral. ( find ſſ dxdy ,…

A: We need to sketch the region between the given  curve and also have to calculate the area using…

Q: Use integration to show that the volume of the closed unit ball B = {(x, y, z) : x2 + y? + 22 < 1}…

A: Let u be the ball.The volume of u is given by the triple integral∫∫∫u1.dV. To compute this, we need…

Q: Consider the double integral S SR x²y dA, where R is the semicircular region given by {(x, y) [x? +…

A:

Q: Find the volume of the region bounded above by the surtace := 2 sin z cos y and bounded below by the…

A: I have done this problem, please check with your answer.

Q: Using Green's Theorem, calculate the area of the region bounded above by y = 5x and below by y =…

A:

Q: Find the volume of the region R.

A: Given, the region R which lies above z=x2+y2 and inside x2+y2+z2=4z.

Q: What is the area of the region bounded by y = x? + 1, x = y² , x = 0, and a = 2? %3D 2 | (2? +1- va)…

A: Use area under curve

Q: Consider the region R bounded by y = x +and y = x - for x 2 1. Sketch the region. Is the area of R…

A: Given, y=x+1x2 and y=x-1x2,  x≥1. Both the curves have the same asymptotes y=x and x=0; by basic…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.