Consider the following. ebr (a) Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radii br and aR. (Let a = 6 and b = 2.) dy (b) By interpreting the integral as an area, find the volume V of the torus.

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Q: Use a triple integral to find the volume of the solid shown in the fig z = 64 – x² – y? 20 60 50 40…

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A: Given:∫π23π2∫03∫r29 r dz dr dθ=∫π23π2∫r29 z03 r dr dθ=∫π23π2∫r29 3 r dr dθ=3∫π23π2  r22r29…

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Q: 9. Fill in the items needed to numerically integrate a function over a volume: bu I = ,f(x, y, z)dV…

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Q: 2) Sketch the solid whose volume is given by the integral  and evaluate the integral. ∫0 to pi/2 ∫0…

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Q: Sketch the solid whose volume is given by the integral and evaluate the integral. 6. 18 r dz d0 dr

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 2xy 03 x < 2 0sys2

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A: We have to write and evaluate the definite integral that represents the volume of the solid formed…

Q: Find the volume obtained by revolving about 0X the area under the catenary y = (a/2)^(e^x/a +…

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Q: Sketch the solid whose volume is given by the following integral and evaluate the integral. S/2/4…

A: Note : φ= constant  , represents a cone  and ρ= constant  , represents a sphere .

Q: (b) (2 pts. each) Set-up only the integral that will give the volume of the solid generated when the…

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 36 – x2 - y² 40 30 20…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 36 – x2 - y² 40 30 20…

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Q: f. Set up (but do not evaluate) an integral with respect to x to represent the volume of the solid…

A: f) To setup an integral which represents the volume of revolution. x=(y-2)2⇒x=y-2⇒x+2=y⇒y=x+2

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Q: 4.² / S² p² sin & dp do dº JTT/2 J1

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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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