ây _ở: x>0, t> 0 where y (0, t) = 1, y (x, 0) = 0. Find the bounded solution of

Q: calculate th integral SSo(x+y) dydx where D is th reigon that deter mined in thees Curves : Y = x, Y…

A: Solution is given below:

Q: 8. The region of integration D is bounded by the lines y = x,x + y ==,y = 0. Show that 1 | sin(x +…

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Q: Express integral I y + x (-4x-2y) -0,x= 1 and y=0,y-1-xto T. of u- dydx in terms of (u)and (v) given…

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Q: 2) a) Ŝ find the value of the inter Specify the integrol liees |-x2

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Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

Q: 3 - Find the bounded ly y=2x-2, x=-1, x= 2 3 area y=2X - 2, x=-I, x= 2 4- Find the anea bondol .

A: Integrate the given parabola from x=-1 to x=2

Q: the volume of a solid bounded by x² + y² = 4,z=1,z = 9-3x-2y using triple integration.

A: We know that the to find the volume of a region by the triple integration V=∫∫∫dv   Where dv=dxdydz

Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: Find the centroid of the region above the X axis that is bounded by the Y axis and the line Y = 3 -…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: 4. The area of the region between the curve y=x* and the line y%3D4 is divided into equal partitions…

A: Given curves are y=x2 and y=4.Also given that y=c divided into equal parts of the area.

Q: 10. The region of integration D is bounded by y = 0 ,y = x² ,x = 1. Show that 1 - sin(1) xsin(y) dA…

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Q: II. SET UP an iterated double integral that will give the volume of the solid bounded by 3x + 2y +…

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Q: Sketch the region of integration. (x, y) dx dy y y (0, 9) |(9,9) (0, 9) (9, 9) y=x y=x

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: Let f(x, y) = 3/x+ 4/y+ 5x + 6y in the region R where x, y > 0. Explain why f must have a global…

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Q: 2. The region bounded by x = 2 y, x = 0, y = 9 is rotated about the y - axis.

A: Given Data: The given curve is x=2y. Rotated about y axis. The limit for y axis is (0, 9).

Q: The path C is a line segment of length 13 in the plane starting at (4,5). For f(x,y)=5x+12y,…

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Q: how do you find the constant needed for rejection region?

A: The rejection region is the set of values of the test statistic (or equivalently the set of samples)…

Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X 2 and the X axis.

A: To find the centroid

Q: Integrate f (x, y) = x over the region bounded by y = x, y = 4x − x^2, and y = 0 in two ways: as a…

A: First draw the graph of line y=x and parabola y=4x-x2. Then find the area of the intersection…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: The path C is a line segment of length 10 in the plane starting at (1, 1). For f(x, y) = 6x + 8y,…

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Q: Let R be the region bounded by the parabola y = x 2 − 1 and the line y = x+ 1 and let f(x, y) = xy…

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Q: Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0)  and then to the…

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Q: Sketch the region of integration. [ [² x√ 1 + y³ dy dx

A: The answer as follows:

Q: Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate…

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

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Q: Find the area and centroid bounded by the curve x=3y-y^2 and the line x+y=3. Graph

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Q: volume of the solid obtained by rotating the region bounded by y=x^2, y=3x about the line x = 3…

A: In this question, the concept of the volume of revolution about the line is applied. Given,…

Q: Use the result of Exercise 37 in Section 6.1 (or the exercise above if your answer is correct) to…

A: Find the volume V of the solid obtained by revolving about the line y=-3 the region between the…

Q: Find F '(x). F(x) = integral of 2/(x+8) dt in interval [x^2,0]

A: Let u=x^2 Then du/dx=2x

Q: 68. Solid bounded above by 3x² + 3y² + z² = 45 and below by the xy-plane

A:

Q: Find the area and centroid bounded by 2x^2+4x+y=0 , y=2x. Graph

A: The region bounded by the curves 2x2+4x+y=0 & y=2x is as shown below.

Q: A thin wire is bent into the shape of a line segment from (1, 2) to (−1, 1), and the curve y = x2…

A: Given: The thin wire with shape as line segment from 1,2 to -1,1 and along the curve y=x2 from -1,1…

Q: Which order of integration is preferable to integrate ƒ(x, y) = xyover R = {(x, y): y - 1 ≤ x ≤ 1 -…

A: Given: fx,y=xyR=x,y:y-1≤x≤1-y, 0≤y≤1 To Determine: Which order of integration is Preferable to…

Q: 4 Set upinbegrl for th volume caboud x- -I y. 12 and

A: Volume problem.....

Q: The volume of the solid obtained by rotating the region enclosed by y = 1/x°, y = = 0, 2, about the…

A: Given:Find the volume of the solid obtained by rotating the region bounded by:

Q: Determine the ordinate of the centroid of the area bounded by the curve x^2 =8y and the line 2x-y=0

A: Given curves are x2=8y and 2x−y=0. We have to find the ordinate of the centroid of the area bounded…

Q: Find the centroid of the region bounded by the curve f(x)= x3 on [0,2] and the x-axis.

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Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X axis.

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Q: Find a center of mass of a thin plate of density δ=1 bounded by the lines y=x and x=0 and the…

A: Given that density is 1 and thin plate is bounded by the lines y = x, x = 0 and y = 30 – x2

Q: How do you find the extrema of a continuous function ƒ(x, y) on a closed bounded region of the…

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Q: Find the centroid of the region bounded by the given curve. x = 5-y2 ; x = 0

A: To find the centroid of the region bounded by the given curves x=5-y2;x=0.

Q: 2. Solve for the centroid of the shaded region. -zolx-1)

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Q: Give necessary and sufficient conditions for p(x)/q(x) to be an immediate integral (do not use the…

A: We want a function of the form

Q: Sketch the region R bounded below by the curve y = x², on the left by the line x = 1 and above by…

A: The region bounded by the curves is as below:

Q: Find the centroid of the region bounded by y = 4x-x and y=-x.

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Q: 3 4

A: