QUESTION 9 Find the maximum value of f(x,y) = 5x + 12y subject to g(x,y) = 0. g(x,y) = x2 + y2 - 1. Round off to two decimal places. QUESTION 10 A region is bounded by y = 0, y = x°, and x = 4. Find the x coordinate of the center of mass. Round off to two decimal places. Remember if A is the area of the region then 1 x = хаydx A QUESTION 11

Q: Question 8 The volume of the solid generated by revolving the region between the parabola r=y2+1 and…

A: The equation of the curves are : C1 :  x = y2+1 C2 : x = 10 Axis of revolution : x = 10 To evaluate…

Q: Question 3 Sketch the region of integration and reverse the order of integration of the integral…

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Q: Example 1 Evaluate [[[16z dV where E is the upper half of the sphere x² + y² +z? =1. Solution Since…

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Q: For the regron x'+y si and you te temperature of the region T3 given by Texiy) = y Find te area of…

A: The temperature of the region is given by, Tx,y=xy The region is defined by below inequalities.…

Q: QUESTION 8 Find the area of the cylindrical surface in Xyz-space where a point (X,y,z) on the…

A: Find the surface area of the cylinder in xyz-space where a point x, y, z on the surface satisfies…

Q: Question 5: Find the volume of the solid bounded by y = x3 +1,x = 0 and x = 3 given that the…

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Q: Question 12 Sketch the region bounded by the following curves and etermine the centroid of the…

A: We have to solve given problem:

Q: Work Problem 2 ( a) Sketch the region of the double integral + edA where R is bounded by a = 3, y =…

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Q: (b) y T= x (p) 3. Region bounded by: y = 4 – x² and y = 0. Rotate about: (a) the x-axis (с) у — —1

A: I have solved the first part for next parts repost the question

Q: Problem 3: Let F = (xy, yz, zx). Let S be the part of the paraboloid z = 1 – x² – y² in the first…

A: (3) Consider the provide question, The curve C is the intersection between the paraboloid and the…

Q: Question 17 Evaluate the double integral y sin(x*)dA R where Ris the triangular region with the…

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Q: Problem #2: Find the mass of the solid bounded by the the graphs ofy 8x2, y = 7, z = 0, and z = 9,…

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Q: Problem 5. In this problem, you wil fnd the volume of the solid genorated by revolving the reogion…

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Q: Question 3 Selve the linear Ruation: dy 3. Integral faualian.

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Q: Question 12 Evalvate the to $2xy dx + (x+y) dy C is the OF y=o direction line integral by applying…

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Q: Given the curve y = (sin x)² 1. Compute the area bounded @ x = 0 to x = 2π.  a. π sq.units b. 2π…

A: Area of the bounded by the curve : If y=f(x) be an continuous function on a,b , then the Area…

Q: Problem 1: Find the volume of the region bounded by the paraboloid z = x² + y? and the cone z = 2 –…

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Q: Question 10 Set up the integral formula that calculates the surface area of the region formed by…

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Q: For the solid region W described and shown in Problem 3, write the limits for fw f dV in the…

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Q: Use the path C given by the parameterization of the unit circle below for these four problems. r (t)…

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Q: Question 8. Use a change of variable to compute the integral 10 R x+ y where R is the triangular…

A: To evaluate the integral by changing the variables x,y into the new variables u,v, use the following…

Q: Problem 15 How far from the y-axis is the centroid of the area bounded by the curve y = x', the line…

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Q: Question 7 Use double integration to find the volume of the solid. 3 3x + 2y + 4z = 12 A) 6 B) 9 c)…

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Q: Problem 10 Use the change of variable technique to evaluate the integral T. (x² + y² Xx² – y² } dxdy…

A: Given integral and region R are,

Q: Question 34 Find the abscissa of the centroid of the region between the parabola y = 6 - x2 and the…

A: As we know that; The expression for the abscissa of the centroid; x=1A∬xdydx Where, A=Area=∬dydx or…

Q: 1.2. The area of the region bounded by the curves sin r, y = cos r, I= 0 and a equal to A. 1.4142…

A: Given curves are y=sinx, y=cosx ,x=0 and x=π/4

Q: Question 1 A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³).…

A: We need to find the integral for work done in pumping the content to a point 3m  from the top of…

Q: QUESTION 1. Sketch the region D that gives rise to the following repeated integral, change the order…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: PROBLEM [ B2 ]: Find the volume of the solid of reolution bounded by the circle z +y = 16, and the…

A: We have to find  The volume of the Solid of revolution bounded by the Circle x2+y2=16 and the lines…

Q: A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration…

A: Introduction :

Q: H.W 1. Find the centre of mass of a thin plate of density & = 3 bounded by the lines x 0, y = x, and…

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Q: Question 5: Find the volume of the solid bounded by y = x³ + 1 , x = 0 and x = 3 given that the…

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Q: Question 3 Integrate f over the given region. Quadrilateral f(x, y) = x/y over the region in the…

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Q: Problem 9. Let R be the region bounded by the curves x = 6y', y = 1, x = 0. The volume of the solid…

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Q: Problem 2: Set up an integral for the volume of the solid resulting from rotating the region…

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Q: QUESTION 10 · D is the region in the first quadrant bounded by y = 2x2 and y = x² + 2. Evaluate the…

A: Definition used-              Double integral -                    ∫D∫f(x,y)dA =∫x1x2∫y1y2f(x,y)dydx

Q: Question# ( 2} Set up the integral that gives the surface area of the solid formed when the region…

A: Given the given region is fx=x2 for 0≤x≤2 is revolved around the x-axis. Apply formula Surface area…

Q: Question Four [5, 6, 6] 1. Show that the surface area of a right circular cone of radius 3 and…

A: I will do que 1 and 3

Q: Question 3 Let D denote the region in the xy-plane bounded by the parabola 4x = y and the straight…

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Q: A particle of mass m in a rectangular box with a fixed volume has ground state energy E(x, y) (x >…

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Q: QUESTION 10 Use cylindrical coordinates to evaluate the integral below. √x² + y²dv, where E is the…

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Q: Question 6 Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 A) 6 B) 9…

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Q: Question 4 Draw the region of integration and evaluate the following integral. LL: 12x2y – y² dydx…

A: We have to evaluate ∫-22∫-x2x212x2y-y2dydx Here we have to first integrate w.r.t y from limits y=…

Q: Question 4: Rewrite the following integral using the order of integration dydxdz CII dzdydx -1-z 1-z…

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Q: (1) Sketch the regions of integration. (a) 7/2 Jo r3m/2 (b) (1r, 0)r drdo 3n/4

A: Consider the equation

Q: Question 5: Find the volume of the solid bounded by y = x³ +1 , x = 0 and x = 3 given that the…

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Q: Ex 16.7.2 Find the center of mass of an object that occupies the surface z = xy, 0 ≤ x ≤ 1,0 ≤ y ≤ 1…

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

A: Volume of revolution

Q: If we rotate the region under the curve y = 8 between x = 2 and x = 3 about the x-axis, what answer…

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