1 Find the centroid of the region bounded by the graphs of the functions y = 2 sin(x), y -x, and and touching the origin. 2 The centroid is at (ã, j) where: y =

Q: 29-32 Use double integration to find the area of the plane re- gion enclosed by the given curves. y…

A: Blue colour = cosh x Red colour = sinh x

Q: find the centroid of the thin plate bounded by the graphs of the given functions. Use d = 1 and M =…

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Q: Let R be the region bounded by y = 6.5 – x, the x axis and the y axis. 6 4 3 2 1 The solid obtained…

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Q: 1. Let S be the triangular region in R3³ with vertices at (2,0,0), (0,6,0), and (0,0,3) with upward…

A: we know that triangular  region is part of plane since all the vertices  ( 2, 0,0)  , ( 0, 6, 0)…

Q: 3. Evaluate the triple integral xyz dV; G is the solid in the first octant that is bounded by the…

A: To evaluate the below triple integral. ∫∫∫GxyzdV Here G is the solid in the first octant that is…

Q: 6. A solid is formed in the first octant bounded by the plane z = 6 – x – y and the cylinder y = 4 –…

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Q: 5. Consider the plate formed by the curve f(x)=x-sin 2x and the x-axis, from x 0 to x= O.B 0.7 0.6-…

A: Consider the given function

Q: Find the centroid of the region that is below y=√x+ 1 and above the x axis, starting at x= 0 and…

A: Calculus

Q: 59. Consider the region bounded by the graphs and x = 1/2. a. Find the area of the region. b. Find…

A: Consider the graph:

Q: y = 4(1-x²), y =1-x² 5. y=

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Q: (a) Calculate the centroid (7, j) of the region under the graph y = cos x for 0 < x <T/2. (b) Show…

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Q: Find the centroid of the region bounded by the graphs of 1 the functions y = 5 sin(x), y and and x =…

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Q: The centroid of the region bounded by y = x, y = -x, and {(cos t, sin t) | st s is (circle one) (0.)…

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Q: 15. a) Sketch the region enclosed by the linex = 3 and y = 1 and the curve xy = 9, %3D and find its…

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Q: Find the centroid x, y, z of the region R cut out of the region 0 < z< 8/x² + y² by the cylinder x2…

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Q: The area is bounded by the curve y = ex, y = e-xand x = 1. (units in meters)  Find the area, in m2.…

A: 1) Given:         curve  y=ex                    y=e-x and x=1   The point of intersection of two…

Q: 2. Consider a hemispherical surface of radius R centred at the origin as illustrated on the right.…

A: Consider  a hemispherical surface of radius R centered at the origin as shown in figure. The…

Q: Let k> 0. SET UP an iterated double integral that will give the volume of the solid formed in the…

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Q: 6] Find the centroid of the region bounded low by y = secz and above by y = 2. ee figure at right.)…

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Q: 17. Find the centroid of the volume generated when the area bounded by y =-x² -x-"and y = -x? -x+ is…

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Q: 9. Find the centroid of the region R in the xy plane bounded by y2 = x and y = 3x

A: Let there are two curves f(x) and g(x). If we divide the region R enclosed by between the curves in…

Q: 9. Find the centroid of the region R in the xy plane bounded by y2 = x and y 3x

A: Given that: y2=x and y=3x. Therefore, we will find the intersection point: x=9x2  (as y2=x and…

Q: Find the centroid of the region bounded by the graphs of the functions y = 5 sin(x), y = x, and x =…

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Q: 2. The region is bounded by x = y² and x = 4-(y-2)² Using horizontal rectangles, set – up the…

A: We need to set up integral to find centroid.

Q: 5.5 Find the volume of the solid bounded above by the graph of f(x, y) = xy sin(x²y) and below by…

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Q: II. Find the centroid of the region bounded by the curves y = cos x, y = 0,x = 0, = x

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Q: 1.  Find the average value of the function y = 2 sin ⁡ x − sin ⁡ 2 x , x ∈ [ 0 , π ] .   2. The…

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Q: 2. a) Sketch the region enclosed by the curves y=-x² +3x and y= x². Hence, find the area of the…

A: We have give curves y=-x2+3x and y=x2its graph is  Now find point of intersection of curves…

Q: 4) Evaluate , z dV using rectangular coordinates, where Q is the solid in the first octant bounded…

A: In the first octant,  x≥0y≥0z≥0    Thus x, y and z cannot be less than 0

Q: Find the centroid of the region bounded by the graphs of the functions 1 and touching the origin. y…

A: Given curve is y=5sinx, y=17x and x=π2. We have to find the centroid x¯,y¯. The formula for the x¯…

Q: 2. Using Green's theorem, evaluate | (ev + 4x°y³ – ya) dx + (xe" + 3x*y? – 3x - :- cos y) dy, aD…

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Q: Find the centroid of the region bounded by the graphs of 1 the functions y = 3 sin(x), y -x, and x 3…

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Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

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Q: 1. Determine the centroid of the first full enclosed region in the first quadrant between sin r and…

A: given curves are                                              f(x)=sinxg(x)=cosx graph of the…

Q: Find the centroid of the region bounded by the graphs of the functions 1 T y = 5 sin(x), y = x, and…

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Q: Find the centroid of the region bounded by the graphs of the functions 1 y = 5 sin(x), y = 2, and a…

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Q: 6) Find the centroids of the shaded region. Indicate the typical rectangles and derive the values…

A: As you post multiple questions  I only answered first one

Q: 89. Find the centroid of the area bounded by y = y = x³,x = 2, and the x-axis 16 =i = %3D 7

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Q: 53. The region in the first quadrant, which is bounded by the curve x² = 4y, the line x = 4, is…

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Q: 1. Determine the double integrals by iteration: f, (x – 3y)dA where T is the triangle with vertices…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: 9. Consider the region bounded by y = x2-4r+5 and y 2. The region is revolved about the y-axis to…

A: To find

Q: find the centroid of the region lying underneath the graph of the function over the given interval.…

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Q: Find the centroid of the region bounded by the graphs of the functions 1 y = 3 sin(x), y and x = 5 2…

A: Given,  y=3sin(x) ,y=x/5  , x=π/2

Q: 6. Consider the solid whose base is bounded by the curve y = x² and y = 2 – x², and whose cross…

A: The given question can be solved as shown in step2.

Q: 2. Find the volume of the solid obtained whe the region bounded by the curve y = sin(x), 0 < x < ™,…

A: For the given information

Q: 55. The region in the first quadrant, which is bounded by the curve y² = 4x, and the line x = 4, is…

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Q: Find the centroid of the thin plate bounded by the graphs of the given functions. Use d = 1 and M =…

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

Q: 5. Determine the x component of the centroid of the given area. y y=x у-1.44-х B A

A: This question is about application of integration

Q: Find the centroid of the region bounded by the graphs of the functions y = 2 sin(x), y = 1 -x, and x…

A: Given curves are y=2sinx, y=x5, x=π2, x=0( touching the origin) At first we find the area between…

Q: 24. Find the counterclockwise circulation of F = (y + e*ln y)i + (e*/y)j around the boundary of the…

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