86. Find the average value of the function f(r, 0, z) = r over the sol- id ball bounded by the sphere r + z? = 1. (This is the sphere x² + y? + z? = 1.)

Q: A region R is bounded by the graphs of y=0.9 Vx and y=0.9x. Find the moments M, and My of R about…

A: y=0.9x and y=0.9x We have to find moments Mx and My and the center of gravity x,y

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: 8. Consider the region R in the first quadrant (x > 0, y > 0) in the ry-plane bounded by x = 2y2 x =…

A:

Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

A: Given,

Q: b. Find the average value of F(x,y,z) = x² + 9 over the cube in the first octant bounded by the…

A: Average value is given by: ∫EFdV∫EdV wherein E is the region as give in first octant. Calculate it:…

Q: Suppose D is the region bounded between the z-axis, the curve y = e", and 0 <I<1. Compute the…

A: We need to compute the integral: ∫∫D2ydA Given that, y=ex and 0≤x≤1.

Q: 12) Find +he integral of the f(xiyia)=x+y? function on the region between the x4y1 and x?+y"= 9…

A: Convert the integral in cylindrical coordinate: ∭Vfx,y,zdxdydz=∫z=01∬1≤x2+y2≤9x2+y2dxdydz…

Q: find the ora of the Region described t vegion bounded by gee"iy=e EIny and

A:

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

A:

Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

A:

Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

A:

Q: Find the average value of the square of the distance from the point P(x, y) in the disk x2 + y2…

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Q: Let f (x) = cos x and g(x) = sin x. Find the center of gravity (x, y) of the region between the…

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Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

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Q: Find the average value have of the function h on the given interval. h(x) = 8 cos“ x sin x, [0, n]…

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Q: Find the average value of the function ƒ(r, u, z) = r over the re-gion bounded by the cylinder r = 1…

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Q: 4. Find the volume of the solid under the surface f(x, y) = xy and above the triangular region in…

A: .

Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1)…

A:

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: Find the average value of f over region D. f(x, y) = 5x sin(y), D is enclosed by the curves y = 0, y…

A: Consider the following function: fx,y=5xsiny D is enclosed by the curves y=0, y=x2 and x=3. Consider…

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

A:

Q: Find the average value h of the function h on the given interval. ave h(x) = 2 cos“(x) sin(x), [0,…

A: Functions

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: Consider the region bounded above by the function z = 1/(x+3)2(y+7)2 and below by the xy plane for x…

A:

Q: Evaluate the following line integral (x + y)ds where C consists of line segments from (0,0) to…

A:

Q: A string of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value…

A: To set up the boundary value problem for the displacement ux,t of string of length L coincides with…

Q: (2) Consider the region D in the ry-plane which is bounded by the following 2 4 curves y =, y = ỷ =…

A:

Q: b. Find the average value of F(x, y, z) = x² + 9 over the cube in the first octant bounded by the…

A: Average value =1Volume of D∫∫D∫F dVVolume of the cube =23=8

Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

A:

Q: Compute the area enclosed by the curve r = Vsin 0 for 0 <o<T. O 1/2 5/2 3/2 O 1

A: Need to find area

Q: Let T, be the approximation using n subintervals for the Trapezoidal rule to estimate I =…

A:

Q: 3/ Find the area of the region enclosed between the curves y= x' and x3 y? مساعدة 1.8 هذا رسم ل…

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Q: need help with 9.2.5

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Q: 5. Evaluate z dV, where E is bounded by the cylinder y? + z2 = 9 and the planes x = 0, y = 3x, and z…

A:

Q: (b) Let F = (-yx², xy²). Let D be the annulus 1 < a2 + y² < 4, and let C be its boundary. Evaluate

A: Value of the given integral is

Q: 3/ Find the area of the region enclosed between the curves y= x' and x= y مساعدة 1.8 هذا رسم ل…

A:

Q: Let D be the region in the xy-plane bounded by x2 + y² = 1 and x2 +y2 = 4, %3D Evaluate S Spf (x, y)…

A: Double integration

Q: | 5z2 dV , where E is Evaluate E the region bounded below by the cone z = Vx2 + y² and above by the…

A: Given: ∫∫∫E5z2dvz=x2+y2x2+y2+z2=1

Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: 2. Find the value of the line integral foF dr without using Green's Theorem, where F(x, y) = (x+y)i…

A:

Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

A: The given function is fx,y=6x+4y. The main objective is to find the average value of the given…

Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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Q: 4/ Find the area of the region enclosed between the curves y= cos 2x , y=0, x=TT/4, x= TT/2 ? ans/…

A: Given-y=cos(2x)y=0x=π4x=π2Let consider that area of the curve is =AWe have two value of x and two…

Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

A:

Q: Find the average value of the function ƒ(r, θ, z) = r over the solid ball bounded by the sphere r2 +…

A: The given function is  fr,θ,z=r