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Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

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Q: The shape for a building that is to become a wheat silo is created by rotating the region bounded by…

A: Given that the shape for a building that is to become a wheat silo created by rotating the region…

Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

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Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 2…

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Q: Find parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y&gt;= 0, in the first octant

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Q: Find the angle of inclination of the tangent plane to the ellipsoid                           x2/ 12…

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Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: 7x + 8y2 and the planex = 3. At what rate is z changing with A point moves along the intersection of…

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Q: Find the vollumes oF the solid that results when the r egion enclosed by the curves y= x, x = y is…

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Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: If the curve y = f(x) , a≤x≤b is rotated about x-axis, then the lateral surface area is given by…

Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: 2. Find the area of surface that is generated by revolving the portion of the curve x = V16 – y , 0…

A: Given, x= √(16-y) Therefore, f(y)= √(16-y) Differentiating the above equation with respect to y we…

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

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Q: Find the area of the surface obtained by rotating the parabola 1 y = 0 <x < 2, about the y-axis.

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Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: Find on equation of the porabola with focus at F (0,-1) and directrix :y=1 in standerd form

A: Find an equation of the parabola in standard form with focus at F (0-1) and directrix : y = 1

Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y-/2) + (1/2, 1…

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Q: # 3 Let act) (cost, sint a is plane Siht) %3D Decide whether not ? curve

A: Given that  α(t)==(cost,sint,sint) Now take α(t)=(x(t),y(t),z(t)) Then, x(t)=cost, y(y)=sint,…

Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

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Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: ston Compute the length of the circle of radius r defined parametrically by x = 3 cost, y = 3 sint ;…

A: given that x=3 cost , y=3 sint; 0≤t≤2π find out the length of the circle of radius r i.e. arc length…

Q: A point moves along the intersection of the elliptic paraboloid z = 2x? + 7y² and the planex = 4. At…

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Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

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Q: If the infinite curve y = eSX, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: The curre y=J36 - z' , -4£ x s4 will be rotated about the ルーaXis. find the area that results af the…

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Q: Suppose the plane So thet its Coordinates are a partile Pir moving in given by y=Fsinzt Plxy) where…

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

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Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y&lt;=2, that lies above the…

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Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: Find the equation of the tangent plane to the given surface at the point (0,-1,2). y = 2x2 – 2 - O y…

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Q: y = x, 0 < x <7

A: The given line  y = (7/5)x This is revolved about x axis  0≤x≤7

Q: Sketch the grapm of the pare cone (6) and Sketeh TE) and valve of f. quaph N't) at the %3D

A: For a vector valued function r→t=a(t)i→+b(t)j→, its unit tangent vector T→t and unit normal vector…

Q: Find the polar eauation for Hhe curve Cartesianm eavation. represented by the given 2.

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Q: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.