I. Set up a triple integral in Cartesian coordinates whose value gives the average temperature of the cylindrical region W bounded by the planes z = 0, z = 2, and the cylinder r? +y? = 1. The temperature distribution is T = f(x,y, z) = 50e+y. Evaluate using the Wolfram Alpha widget. (Ans: 85.9) 1

Q: Find the center of mass of a thin plate of constant density 8 covering the region in the first and…

A:

Q: Find the volume created when rotating the area contained by the x – axis and the given parametric…

A: Solution:-

Q: The curve C is the portion of the graph of y = 16 for 0sz5 2 (distances measured in m). The curve C…

A: The function given to us is as follows: y=116x4⇒x4=16y⇒x=2y14 Where, 0≤x≤2. For x=0,  y=0. For x=2,…

Q: The area in the first quadrant, bounded by the curve y = 2x1/2, the y-axis and the line y – 6 = 0 is…

A: The centroid of volume of solid revolution about the line y=k is obtained by the following formula.…

Q: Consider the given curves to do the following. x+y=6, z=15-(v-3)² Use the method of cylindrical…

A:

Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

A: Given slant height l. Let r and R be the radii of the frustum. Let h be the height of the frustum.…

Q: Find Ix, Iy Io X, and y for the lamina bounded by the graphs of the equations y = Vx, y = 0, x = 4,…

A: INTRODUCTION: The formula of the radius of gyration of the lamina of the density function ρ is given…

Q: Find the exact coordinates of the centroid for the region bounded by the following curves: = 16x, 9.…

A:

Q: Find the surface area generated by revolving the curve C : x(t) = 3t, (0 < t < 1) y(t) = 2t about…

A: Use the formula for the surface Area when a parametric curve rotated about y-axis.

Q: 9. Find the characteristics of the equation hx = bd and determine the integral surface which passes…

A:

Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

A:

Q: Calculate the total mass of a metal tube in the helical shape r(t) = (cos(t), sin(t), 1²) (distance…

A: rt=&lt;cost, sint, t2&gt; (distance in centimeters)0≤t≤2πδx, y, z=9z g/cm

Q: Use a Riemann sum to find the area of the trapezoid bounded by the lines y = 0, x = 1, x = 2, and y…

A:

Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by 3 T…

A:

Q: 6. Determine the volume V of the 3 dimensional lampshade formed (see diagram below) by rotating the…

A: This is area by integration question

Q: = A wire has the shape of a helix with parametrization x = t, y : 2 cos(t), z = 2 sin(t) for 0 ≤ t ≤…

A:

Q: Find the moment of inertia with respect to the y-axis for the area bounded by y = cos²x³, x = 0.2…

A: To find the moment of inertia with respect to the y-axis for the area bounded by the below curves.…

Q: tind Value to the jAtegrals: -3 7 Sec 7 dz Yis the triangle with Vertices at. the foints 7- 7. ら 2.

A:

Q: Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y + 2

A:

Q: State the characteristics (type, order, degree) y y" - V1+ (y')² = 0

A:

Q: 5. A heavy rock blown straight up from the ground by a dynamite blast. The velocity time t during…

A:

Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: Determines a e R so that F- dr = -2 – 4 Where F(x,y) = ay, 2 e C is the part of the circumference…

A:

Q: Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

A: Given that the differential equation ydx+xdy1-x2y2+x dx=0