The surface area of the surface generated by revolving y=1-x² for 0

Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = secx about…

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Q: The area of the region bounded by the curves y =x and y = 20 –x² is drx|-'א-0 'J - »4,4 - S** |20…

A: We will use double integration to find area

Q: We must integrate y = (8x-x2)-(2x) = 6x-x². The limits on the integral correspond to the smallest…

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Q: Find the area bounded by the curve x = (y+1)2 and y+1 = x2. Show complete solution of points of…

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Q: y = V(4x – x²) (1+0.25x + 0.25 sin(x))

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Q: Find the 1st quadrant area bounded by y = vx – 2, X and x = 11 Provide a sketch; show 2 solutions…

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. [x x cos…

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Q: Find a center of mass of a thin plate of density 8 = 6 bounded by the lines y=x and x = 0 and the…

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 7x…

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Q: 4. The area of the region between the curve y=x and the line y=4 is divided into equal partitions by…

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. |x cos…

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Q: Find the area of the surface generated by revolving the curve on the indicated interval about the…

A: answer is mentioned below

Q: consider the equations: y=x2 and y = -x2 -x +6 1) Sketch both curves of the given equations on the…

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Q: 4. The area of the region between the curve y=x* and the line y%3D4 is divided into equal partitions…

A: Given curves are y=x2 and y=4.Also given that y=c divided into equal parts of the area.

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Given: ∫(1,0,0)(0,1,1)sinycosxdx + cosysinxdy+dz To Show: (a). Differential forms in the integral…

Q: integral arctan (1/x)dx

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Q: FIND THE CENTROID OF THE REGION IN THE FIRST QUADRANT BOUNDED BY THE GRAPH OF y=9-x2, THE X-AXIS,…

A: Given region is bounded by the graph of  y=9-x2, The X-axis and Y-axis

Q: 24) Using Numerical Integration to estimate area between curve (y=2-x²) and line (y=-x), with n=3

A: We have y=2-x2, y=-x then intersection point is -x=2-x2 ⇒x2-x-2=0 ⇒ x2-2x+x-2=0 ⇒ (x-2)(x+1)=0⇒x=-1,…

Q: volume of solid of as revolution y^2=4x and x^2=4y about the x axis

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Q: Find the area of the surface formed by revolving y = x³ on 0 < x<1 around the x-axis. Show all steps…

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Q: volume of the solid obtained by rotating the region bounded by y=x^2, y=3x about the line x = 3…

A: In this question, the concept of the volume of revolution about the line is applied. Given,…

Q: Find the volume of the solid generated by revolving the region in the first quadrant bounded above…

A: We want to find the volume.

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: Solution.

Q: 8. cos x sin y dx +(3xy+sin x cos y) dy and y = \x 4oil C:boundary of the region lying between the…

A: Given that ∫Ccos x sin y dx+(3xy+ sin x cos y)dy ;y=x4, y=x Using Green's theorem ∫CP dx+Q…

Q: sketch the described regions of integration. 1 ≤x ≤ e2, 0≤ y ≤ ln x

A: Given  1 ≤x ≤e2 , 0≤ y ≤ ln x

Q: Consider the curve segments: 1 S1: y = x from x = to x = 2 and 2. %3D S2: y = Väfrom x = to x = 4.…

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Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x)=64-4x^2…

A: Given query is to find the volume of the solid generated.

Q: Integral of sinh(e^lnarccot3x)dx/(1+9x^2)

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Q: Find the area of the surface resulting from rotating the curve given by y=(1/4) x2 - (1/2) ln⁡x,…

A: you can clearly understand if you follow the below solution

Q: Double of Integration of square root of 25-x²-y² with respect to x bounded by (0,3) and with respect…

A: The given integral is

Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

Q: A hole of radius 3 is bored through the center of a sphere of radius 5. Let the cross- section of…

A: we will draw region which can be rotated to create solid region whise volume needed to find . Then…

Q: The volume of the solid generated by the curve y = e¯*, between x = 3 and x = 8 about the axis is -…

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Q: THE REGION BOUNDED BY y = 205x - 1 AND THE X-AXIS IN THE INTERVAL πT 317 EX2 IS REVOLVED ABOUT 2 2…

A: The Shell formula for Revolution about a vertical line is used to evaluate the volume of the solid…

Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: 1. The edge of a cube was found to be 32 cm with a possible error in measurement of 0.1 cm. Use…

A: Given : Measurement of edge of cube a = 32 cm Possible error in measurement of edge is da = 0.1 cm…

Q: The volume of the solid obtained by revolving the region enclosed by the curves y = 7 - x2, y = 0, x…

A: Given: The region is bounded by following curves: y=7-x2x=0y=0x=2 And an axis of revolution is x=3.

Q: Find the area of the surface obtained by rotating y = cosh x over [−ln 2, ln 2] around the x-axis.

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Q: Find the indefinite integral using integration by parts with the given choices of u and dv. x cos 9x…

A: Integration by part ∫u dv=uv-∫du v where u and v are the function x

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Here, we have   Assume ∫(0,0,0)(2,3,-6)2xdx+2ydy+2zdz                   (i)   Using the formula,…

Q: Find an approximation of the area y = 16 - x² over the interval [0,4] using L6 (left end point…

A: Use: Area=∆xf(x1)+f(x2)+f(x3)+f(x4)+f(x5)+f(x6)       where ∆x=b-anwhere n= no. of rectangle…

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

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Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3)…

A: Given : ∫( 0 , 0 ,0)( 1, 2, 3)  3 x2y dx + ( x3 - z3 ) dy - 3y z2 dz

Q: The volume of the solid obtained by revolving the region bounded by the curve y = x - x² and the…

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Q: Find the area of the surface obtained by rotating the curve y = ln(1 — x2), 0 ≤ x ≤ 1/2 about the…

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Q: Q3. The region bounded by the curve y x² and the line y = 3x, is revolved about the line x = -3.…

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Q: Find the differential equation of the family of spheres of radius r with Centre on the xy-plane

A: General form of the equation of the sphere with radius r and center on the xy plane is given by…

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

A: Find the area of the thin plate, it is equal to the area enclosed by cos(x) and x-axis over the…