y = 2x, y = 3x - x 7) A region is bounded by c) Rotate around the line x = 5 b) Rotate around y = 4 Use methods a) Rotate around the x-axis any you want

Q: Evaluate SII xdv, where Dis the region bounded by x-yz-0, X=0, 2•0, and yol. y=x+2 (back)

A:

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

A:

Q: Sketch the planar region bounded by y = x³, x +y = -2 and y = 0. Find its area.

A:

Q: Region bounded by y = x* +2, y = x+4 rotated about the x-aKis 2.

A:

Q: By using double inpegrals, Find Ihe area the enclosed by of region b) cur ve x:- yo, Line e) curve…

A:

Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

A:

Q: sketch the regions bounded by z=0.67 and z=1.56 and find its area. show your solution in your paper

A: The standard normal distribution is a bell shaped distribution which is centred at the mean 0. The…

Q: Find the area of the plane region bounded by y = x2 - 4x and y = x(2 - x)

A:

Q: 2. Region bounded by y= x, x=0 and y=15, rotated about the y-axis

A:

Q: Show the triangular region bounded by the lines x = 0, y = 0 and x + y = 1 is invariant for the…

A: Given: It is given that, the triangular region is x=0, y=0 and x+y=1. To prove: We have to prove…

Q: Sketch the region enclosed by the given curves. y = 3/x, y = 12x, 1. y = -X, 3 x >0 y y 8- 6. 6. 4 4…

A: Given curves: y=3x, y=12x, y=x3 Andx&gt;0

Q: integrate ƒ over the given region. ƒ(u, y) = y - √u over the triangular region cut from the first…

A: Given  The function is ƒ(u, y) = y - √u . The triangular region cut from the first quadrant of the…

Q: 3. Region bounded by Y = rotated about the x-axis ,x=0 and y=15,

A: By shell method

Q: Find area of the region bounded by x2 + y2 = 32, 6y = -7x and 15y = 4x where y > 0. Leave your…

A:

Q: 4. Region bounded by y = x2, x=0 and y=15, rotated about the y-axis

A: Imagine the plot and rotate it about the axis specified and the resulting figure will lead to the…

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

A:

Q: the voulme of the region are  bounded by the paraboloid x= y^2+z^2 and the half cone x=…

A: The volume of the region bounded by the paraboloid x= y2+z2 and the half cone x= 8y2+z2

Q: integrate ƒ over the given region.Quadrilateral ƒ(x, y) = x&gt;y over the region in the first…

A: Given,

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: (1) y = x, y = 2- |x| (2) y = 1/x², y = 8x, y = x/8

A:

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

A:

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A: Solution is given below:

Q: Show that the area of the plane region bounded by the curves,  x - y =7   and    x= 2y² - y + 3…

A:

Q: 4. у%3D 2х—х2, y = 2x² – 4x

A:

Q: – 4V5 )ds]

A:

Q: Sketch the region enclosed by the given curves and find its area. у — y = 1/x, у — х, у—x, х>0

A: The given curve is: y=1xy=xy=14xx&gt;0  Sketch the region enclosed by the given curves and find its…

Q: Calculate f 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2

A: Given integral is ∬R4ydydx, where R is a region bounded by the curve y=x2 and y=−3x2−2. We have to…

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A:

Q: 6 Find the center of mass of a thin plate of constant density & covering the region in the first and…

A: Calculate center of mass for x coordinate: x=∫x=01∫y=-61+x261+x2xdydx∫x=01∫y=-61+x261+x2dydx…

Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

A:

Q: D be the region that consists of points (x, y) such that x² + (y - 3)² ≤9. Then, (x² + y²) dA equals…

A: see my solution

Q: Sketch the region enclosed by the given curves andfind its area.   x=y 4 ,y = √(2 - x)   ,y = 0

A: x=y4,  y=2-x,  y=0. The graph is,

Q: Evaluate the line integral | (x + 3y + )ds, where Cis the line segment joining the origin with the…

A:

Q: (Choose from: a. Disk Method, b.Washer Method, c. Shell Method, d. Disk and Washer, e. Disk and…

A: Given that, y = x2 ; x = 0; y = 15 3) Volume of the region bounded by the given curve rotated about…

Q: Sketch the region which is defined by the given condtions. 0 ≤ θ ≤ π, r ≤ 3

A:

Q: Evaluate the line integral | (x + 3y + 2)ds, where Cis the line segment joining the origin with the…

A: Solve integral.

Q: Sketch the bounded region enclosed by 2y = 4/x, y = 3, and 2y + 3x = 7, then %3D find its area.

A:

Q: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

A:

Q: Evaluate the line integral ∫Cx^3z ds, where C is the line segment from (0,3,8) to (8,4,6).

A:

Q: 1. Region bounded by y= x, x=0 and y=15, rotated about the x-axis

A: Volume of solid revolve around y axis

Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point…

A:

Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: rotate the region bounded by y=sqrt(x), y=3 and the y-axis about the y-axis

A:

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y-y3, x…

A: Consider the graph:

Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

A:

Q: region bounded by y =x1/2 , y = 0 and x = 9. Use disks or washers to find the volume generated by…

A:

Q: find the are of the plane region bounded by the urves y=3x2 and y=16-x2

A:

Q: Sketch the region enclosed by the given curves. y = 8 cos(x), y = 8 - 8 cos(x), 0<x T

A: This question is related to area bounded by curves, We will use integration to solve it.

Q: Find area of the region bounded by x2 + y2 = 6?, 5y = -7x and 2ly = %3D 11x where y > 0. Leave your…

A: The region bounded by x2+y2=62, 5y=-7x &amp; 21y=11x where y ≥0

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.