Consider the region between the graphs of f(x) = 5 – x and g(x) = 2x on [1,4]. For each line of rotation given in Exer- cises 45 and 46, use definite integrals to find the volume of the resulting solid. 45. Around the x-axis 46. Around the line x = 1 y 8 8 6. 6- 4 4 2 + 1 2 3 2 3 4 -2 -2 -4 -4 -6 -6 2. 638

Q: The region bounded by the curves y = x² – 3 x and y = 4 x is revolved about the line y = -4. Which…

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Q: Evaluate the tripple integral of f(x,y,z) = sin(x2+y2)  over the solid cylinder with height 5 and…

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Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

A: We first sketch the region using a graphing calculator.

Q: ON Verify Green's Theorem by evaluating both integrals 7y dx + 7x*dy = J J]a дм ƏA for the path ду…

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Q: Define R as the region bounded by the graphs of f(x) = 3√x and g(x) = over the interval [1, 3].…

A: Given thatRegion bounded by y=x28 , y=3xx=1 and x=3Using cylindrical shell mathod…

Q: Which of the following integrals represent the area of surface obtained by rotating the curve y= =…

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Q: 2. Consider the following graph of x = F(y) and x = G(y). 2- The orange curve is F and the purple…

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Q: m #12: Find an integral which represents the volume of the solid obtained by rotating the region…

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Q: 2) Calculate the integral the regions descri bed. over / 2x- 5xy- 3y² dA. On a y = (x-1) /3 , y= -2x…

A: Bounding lines y=x3         → 3y-x=0y=(x-1)3→3y-x =-1y=-2x    →y+2x=0y=1-2x  →y+2x=1

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: Consider the region bounded by the graphs of y = 3* – 1 and x = y? – 3, illustrated at the right.…

A: Given: Region bound by the graphs y=3x-1 & x=y2-3 The given region is homogeneous, i.e., density…

Q: The integral: 2nx coS x dx represents the volume of a solid obtained by rotating the region: A)…

A: We have to find the region that is rotated.

Q: 11. xyz dV, where G is the solid in the first octant that is bounded by the parabolic cylinder z = 2…

A: To evaluate the triple integral

Q: Given the domain 9 = {(1, y) | − 4 ≤ x ≤ 4, - 4 ≤ y ≤ 4}:: D the double integral of f(x, y) = 1 over…

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Q: 3. Give iterated integrals describing II, z² Vx2 + y² dV_ E where E is the region in the first…

A: Given the iterated integral ∫∫∫Ez2x2+y2 dV. Here E is the region in the first octant inside the…

Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

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Q: Match the following integrals with the solid whose volume it represents. 36 T/2 Α. π cos (x) dx В. п…

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Q: Consider the region formed by the graphs of y = e^x , y =0 , x = 2 and x = 4. Which integral…

A: We sketch the region using a graphing calculator The shaded region is rotating about the y-axis The…

Q: The volume of the solid generated by revolving the region above around the line y = -5 is .2 (A) *…

A: In the question it is asked to find integral for volume of solid generated by revolving the region…

Q: Evaluate the integral [[[var !!! y² dv where G is the solid in the first octant that lies below the…

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Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: 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: Consider the rectangle [0,1]*[0,1), its dersity is given by plx.y)=Ke** if we Know that " (Ke** )…

A: Given: Density ρx, y=kex+y∫01∫01kex+ydxdy=ke-12……1   Dimension of rectangle is 0, 1×0, 1   To find:…

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 an expression for the volume V of the solid of revolution obtained by rotating the region…

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Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: Evaluate the triple integral. 7xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: 3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region…

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Q: y? = 1? Which of the following integrals represents the length of the upper half of the ellipse 25…

A: Topic = Application of integration  Correct answer = A

Q: problem in photo attached

A: The given curves are,

Q: Evaluate |// e-V where E is the region between two cylinders z + = 4 and r +=9 with 1< y55 and : <0…

A: We will find out the required value.

Q: Evaluate the triple integral. III. 7z dv, where E is bounded by the cylinder y2 + z² = 9 and the…

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Q: The volume of the solid generated by revolving the region between the parabola x =y²+1 and the line…

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Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: The solid E bounded by the equation 9x^2 + 4y^2 + z^2 = 1 and located in the first octant is…

A: Given : Equation of sphere is 9x² + 4y² + z² = 1

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

A: Consider the given integral is∫∫Rx2+2xydydx and R is the region bounded below by y=x2 on the left of…

Q: Define R as the region bounded by the graphs of f(x) = 2√x and g(x) = over the interval [0, 1].…

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Q: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

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Q: 2. Assuming that G is a plane region located between the graph of the cubic function (y=x^3) and the…

A: The given integral is ∫∫G12xy dA and the graph of the cubic function y=x3 and the lines x=0, y=1 A…

Q: 3. Find the centroid of the region bounded by y 3-e, y0, 0, and 2. Since 0, z = 0, and x-2. Since…

A: The given region is bound by three straight line i.e. y = 0, x = 0 and x = 2 and one curve y =…

Q: Evaluate the triple integral. III. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the…

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Q: A) If the volume (1) of the region (D) enclosed by the surfaces (z = x² + 3y²), and (z = 8 – x? –…

A: Answer A:   The intersection between surfaces: x2+3y2 = 8 - x2 - y2 2x2+4y2 = 8 x2+ 2y2 = 4 (x/2)2…

Q: 3. Find the volume of the solid under the plane 3x+ 2y – z = 0 over the shaded region between the…

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Q: Can you help me solve and understand number 24. Thanks

A: Obtain the region bounded by the curves and the limits as follows.

Q: Evaluate the triple integral. 5xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Given that z=1+x+y The range of the variables are, 0≤x≤10≤≤x0≤z≤1+x+y Then, the integral is,…

Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

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Q: Give the limits of integration for evaluating the integral s(1r,8, z) dz r dr de as an iterated…

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Q: Consider the region in the first quadrant, bounded by the curves y=x^3, y=x^(1/2). For each of the…

A: Given curves are y=x3y=x

Q: Consider the curves y = x" + 1, y = 2, and a = 0. Set up the integrals for the following. The volume…

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