Find the moment of inertia of the area in the first quadrant bounded by the curves y = 9 – x² and y = 3x – x2 about the y-axis -

Q: Find the moment about the x-axis of a wire of constant density that lies along the curve y = x3 from…

A: Find the moment about the x-axis of a wire of constant density that lies along the curve y = x3 from…

Q: where y=f(x), 8y^2 = x^2-x^4 , of the curve segment X-axis write the surface area of ​​the rotating…

A:

Q: Determine the moment of inertia about (a) x-axis and (b) y-axis, the area bounded by y? = 4x and x?…

A: Ans:-   we  have to determine the moment of inertiaabout  a  x‐axis  and  b  y‐axis, the area…

Q: Solve for the moment of inertia with respect to the y-axis for the area bounded by the curves, y? =…

A: follow next step

Q: Find the moment of inertia about the x-axis and y-axis of the area between the function and the…

A: ρ = constant densitym = mass of objectI   = moment of inertial Iy = I Around y-axis:Iy =∫x2dmIy =…

Q: Find the moment of inertia with respect to y-axis the area bounded by x2- 4y + 8 = 0, the lines x =…

A: The given question can be solved as shown in step 2.

Q: Find the moment of inertia with respect to x- axis of the area between y = sin x from x = 0 and x =…

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Q: Find the Moment of Inertia for the area bounded by the parabola x2 + y = 1 and the coordinate axes…

A: Graph of the given equation: x2+y=1 Since we have to find the moment only  for the 1st quadrant…

Q: Find the moment of inertia of the region between the parabola y=4-x^2 and the line y=1-2x from x=0…

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Q: express the length of the curve as an integral but do not evaluate it. r = eθ + 1, 0 ≤ θ ≤ π/2.

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Q: Find the moment of inertia of the area bounded by the curve x^2 = 8y, the line x = 4 and the x-axis…

A: Given curves are x2=8y, x=4 and the x−axis. We have to find the moment of inertia of the area…

Q: Find the moment about the x-axis of a wire of constant density that lies along the curve y = 2x from…

A: Moment about x-axis is given by the formula.

Q: ASAP PLZ Find the moment of inertia with respect to x-axis of the region in the first quadrant,…

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Q: Find the moment of inertia about the​ x-axis of a thin plate bounded by the parabola x=2y-3y2 and…

A: Given that the equation of the parabola,x = 2y – 3y2and the equation of linex + 7y = 0

Q: Find the center of mass and the moment of inertia about the​ y-axis for a thin rectangular plate cut…

A: Given that density = x + 2y + 4 and rectangular plate is bounded by the lines y =1 and x = 6

Q: Determine the moment of inertia of the area bound by the two curves about the x and y axis. y y = x?…

A:

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A:

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

A:

Q: Find the moment of inertia with respect to y-axis the area bounded by x2- 4y + 8 = 0, the lines x =…

A:

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 4y - y² and y =…

A: Let's find moment with respect to you axis.

Q: ) Find the area of the surface that is obtained by rotating the curve Y = 0.25X² – 0.5 Log.X, 1<X<2…

A:

Q: Find the moment of inertia of the area bounded by the curve x2=4y, the line y=1 and the y-axis on…

A:

Q: Find the Moment of Inertia for the area bounded by the parabola x + y = 1 and the coordinate axes in…

A: Solution :-

Q: I = (4xy' + (y')²)dx

A:

Q: Find the moment of inertia with resped to the y - axis of athin sheet of constant density s=1 gm/cm?…

A: To find the moment of inertia

Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: Evaluate the area under the parametric curve given by x = 2, y = 4t – 2 and above the x-axis on the…

A: Area of the parametric curves along x+axis

Q: Find the area of the surface obtained by rotating the curve y = V1+ e, 0sx<1 about the X-axis. 2).…

A:

Q: Find the moment of inertia with respect to y-axis the area bounded by a²y = x³ , the x-axis, and the…

A: Given....

Q: y = f(x)impending, 8y² = x² – x*, sxs- calculate the surface area of the rotating V3 body formed by…

A:

Q: Find the surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: 1 y = f(x) impending 8y² = x² – x*, V3 1 To Find: Surface area of the rotating body formed by…

A:

Q: Find the moment of inertia for a quarter of a regular circular plate of radius (b)Find Mom ent of…

A: Given: (a) A quarter of a regular circular plate of radius (b) The parabola Y=x2b and the line y=b

Q: Find the center of gravity of the region bounded by the x-axis, the curve y = sec x, and the lines x…

A: Consider the given question,The graph of the curve y = sec(x) and the line x = -pi/4, x = -pi/4 is…

Q: Determine the moment of inertia with respect to oy the area bounded by y^2=2x and the line x-y=0

A: According to question,y2 = 2x,x-y = 0

Q: Find the moment of inertia of the area bounded by the given curves with respect to the specified…

A:

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = =9y-y2 and y = 2

A: Follow the steps.

Q: Find the moment of inertia of the area bounded by the curve y^2 = 4x, the line y = 4, the y-axis on…

A: Moment of Inertia about x-axis

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

A:

Q: Find the moment of inertia with respect to the y-axis of the area bounded by the curve y=1-x3 and…

A:

Q: Find the surface area of revolution about the x-axis of 3 sin(7x) over the interval 0 < z <

A:

Q: Find the moment of inertia of the area bounded by the curve y^2 = 4x, the line x = 1, the x-axis on…

A: Given: The area bounded by the curve y2=4x, the line x=1, the x-axis on the first quadrant with…

Q: Q4: Evaluate the surface area of the object obtained by rotating 1+ 1² dx x = √√√y +5, √5 ≤x≤ 3,…

A:

Q: Q8: Find the moment of inertia about the x & y axis for the area bounded by the curve y= e" and the…

A:

Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

A:

Q: Find the moment of inertia with respect to y-axis the area bounded by a2y=x3, the y-axis, and the…

A:

Q: Find the moment of inertia with respect to x-axis the area bounded by 2y2 - 8y - 16x + 16 = 0 and…

A: The solution are next step

Q: Find the surface area of the curve f (x) = x over [1,2| rotated .3 3 about the – axis -

A: The revolution of the curve y = f(x) around the x-axis is: S=2π∫abf(x)(f'(x))2+1dx

Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: Consider the given integral as  2π∫-5581-x2dx

Q: Find the surface area of revolution about the x-axis of y = 6 sin(7x) over the interval 0 < x < 7

A: Here we have y=6sin(7x)  We have to find surface area of revolution about x axis in interval 0 to…