y = x², y = 2x, about the line x = 2 using the method of disks or washers. 4 Volume (sqrty)^2-(1/2y)^2 dy /- 8/3pi

Q: of the regioh in the first Guadrant, Find the Carea bannded line on the left by the y-axis, below by…

A: Find the point of intersection of  by equating the “y” of both the equation, consider only the…

Q: Find the area of the segment cut off from the curve y = sin x, 0 ≤ x ≤ ¹ by the line y = 1/√2. 3r 4…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y3…

A: We know that area of surface generated by revolving the curve y=f(x) about x-axis from x=a to x=b is

Q: Find the between the two curves. area 2. X=ay, a'y=x 3

A: The area between the curves can be calculated by integration. The formula used for the integration…

Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: The area of the surface obtained by rotating the curve y = 21 x + 1, 0sx< 42 about the x-axis is

A: Given:- y = 21x+1 To find:- Are of rotation about x axis [0, 42]

Q: Find the tangent to y = cotx at x = - T O A. y = - 2x + 2 π +1 +1 OB. y=2x-- OC. y=2x+1 OD. y=-2x +…

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Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

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Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: dx 4.Exaluate I=| correct to three decimal places by Trapezoidal rule with h=0-25.

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Q: Q6/ Find the moment of inertia and radius of gyration about the x-axis of a thin plate bounded by…

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Q: Q: Find the equation of the tangent plane to the surface:- z-Ln(xj) -x5J , atthe poit (7,4)

A: The given surface is z=lnx2y-xy=fx,y at the point -12, 4. The equation of tangent plane is…

Q: A particle follows the trajectory x(t) = 3 + 2t, y(t) = 10t – t2 with t measured in seconds and…

A: Given: xt=13t3+2tyt=10t-t2

Q: Find the area of the segment of a sphere formed by revolving the graph of y = √25-x2,0 sxs 4, about…

A: Given y=25-x2, 0≤x≤4 A sphere is a geometrical object that is a three-dimensional analogue to a…

Q: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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Q: Find the area of the segment cut off from the curve y = sin x, 0≤x≤ n by the line y = 1/√2. H4 34 y…

A: Let's find area of segment.

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the area bounded by the curve y = 16 A 16 square units (B) 8 square units 10 square units 4…

A: Find the area bounded by the curve y= 1/16x3-3/4x2+3x and the line y= x .

Q: b) Find the shaded area of diagram that shecked by curve y =x² + 2x and the line y

A: The area between curves y=f(x) and y=g(x) on an interval [a, b] where f(x)≥g(x) on the interval is…

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: Find the length of the curve.y=x3+14x,1≤x≤2. Round the approximation to 4 decimal places.

A: The length of the arc from point a to b is given by:

Q: The area of the surface obtained by rotating the curve y = 25-x² , -4 sx<4 about the x-axis is

A: Area of the surface rotated about x -axis is, a≤x≤b,…

Q: ind the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Find the area bounded by the curve y= 16 (A) 8 square units (B) 4 square units (C) 10 square units…

A: To find out the bounded area by the curves.

Q: The region in the first quadrant bounded above by the line y = 6, below by the curve y = √6x, and on…

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Q: find the value of c that the line y=3/2x+6 is tangent to y=c(sqr-root x)  c=

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Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

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Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = V 25 - x2, 0 sx< 4,…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A: The above problem is solved.

Q: A thin plate of constant density d = 1 occupies the region enclosed by the curve y = 36/(2x + 3) and…

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Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

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Q: Find the area bounded by the curve y = 16 (A) 16 square units B 8 square units C 4 square units D 10…

A: Given  y = x316-34x2 + 3x  ------(1) y =x                             -------------- (2)

Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

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Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. y=…

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Q: Find the area bounded by the curve y=- 16 A 10 square units B) 16 square units Ⓒ 8 square units (D)…

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Q: Find the area of the segment of a sphere formed by revolving the graph of y = V9 - x2, 0 sxs 2,…

A: We need to find area.

Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

Q: s to the curve y = x* at the %3D

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Q: Q2: Determine the tangent plane and normal line to the surface x^2+2xy-y^2+z^3=7 at point (1,-1,3)

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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Q: integrate ƒ over the given curve. ƒ(x, y) = x2 - y, C: x2 + y2 = 4 in the first quadrant from (0, 2)…

A: The given curve C is a circle with center at origin and radius of 2 units. Let the parametric…

Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

Q: Find the acute angle between the curves y = x2− 2x and y = ex − 1 at the point (0, 0).

A: To find the acute angle between the curves y=x2-2x and y=ex-1 at the point (0, 0)

Q: Find the area bounded by the curve y=-x³ 1 - 16 A 8 square units B 16 square units 10 square units 4…

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