The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3 %3D 12 O 2T dx O 2m (24 – x) O 21 (24 – x) (24 + x) () dx O 21 dx O 2n (x - 24)

Q: A) S16 S cos (16r x) dx dy. Osxs 2 Os ys x* B) Find the area between the parabolas x = y -1 and x =…

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Q: Evaluate the integral (2x+3y) dx + (6x – y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

A: To Evaluate: I=∫C(2x+3y)dx+(6x-y)dy along the parabolic arc y=x2 from (0,0) to (1,1).

Q: Evaluate the line integral f y(tan x + x sec² x) dx + x tanæ dy + dz once around the circle x² + y²…

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Q: Find the differentlal dy of the glven function. (Use "dx" for dx.) y = BVx + dy =

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Q: Sketch the region that lies between the curves y = 4 sin(x) and y = 3 cos(x) from x = 0 to x = 0.37.…

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Q: Q3) Evaluate triple integral N S dz dx dy . x-y

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Q: Evaluate the integral. 3 4x A y cos z dx dy dz 0 0 0 3 4x A I ly cos z dx dy dz = U 0 0 0 (Type an…

A: We have to find

Q: Evaluate the integral (2x – y) dx + (x + 3y) dy along the path C. C: x-axis from (0, 0) to (0, -3)…

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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: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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Q: The vahe of the integral fx*dx with step length 0.5 using Trapezoidal's nule is a) 0.375 b) 0.875 c)…

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Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0) = 0. Find its maximal interval of existence %3D

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Лу — х dy y? -dx + (1,2) Moreover…

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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: The volume of a right circular cone of radius x and height y is given by V = volume of the cone is…

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

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…

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Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: Evaluate the integral (12x + 15y)dx + (24x – y)dy along the paraboli arc y = x from (0,0) to (1,1).…

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Q: -2y The line integral (e sin x) dx+(x' +3y)dy with path F (t)= (8cost, 8 sint) such that 0sts2n. Set…

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Q: The area of the region between the curve y = xr? – 6x +8 and the x-axis & r = 0 ; x = 3 is given by…

A: here option c is true because we will take the area in x -axis so will take limit of x and integrate…

Q: line integral x³ dy), where y is t 3 X counter clockwise.

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Q: Q2: Find the surface area generated by rotating for y = x² - ln(x) for x = [1, 2] about the y-axis.

A: We need to find Surface area.

Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Evaluate the line integral curve C′ : x = 4 cost, y = 8 sint (0 ≤t≤7) NOTE: Enter the exact answer.…

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Q: 3. Find the area of the region that lies inside both curves: r = sin 0,r = cos 0 0.8 0.6 0.4 0.2…

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Q: Find the real number a for which the value of the iterated integral V1- (y- (-2²- ỷ +2y) dx dy a-1 -…

A: Let fx,y=-x2-y2+2y. To determine the maximum value of the function, differentiate f(x,y) partially…

Q: Set up an integral for the length of the curve. y = x°,0< xs 1 1 V1 + 6x5 dx V1 + 6x10 dx V1+ 36x10…

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Q: B)evaluate the line integral: $5xy'dx- dx +x'ydy where c: y = x; y= x

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Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

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Q: 5. Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

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Q: V = 200 /R volts in free space in the region bounded by 2mm <R <3mm, 0 <8 <n / 2 and 0 <o <n / 2…

A: Given 2 mm&lt;R&lt;3 mm, 0&lt;θ&lt;π2 and 0&lt;ϕ&lt;π2 Now, 2×10−3 m&lt;R&lt;3×10−3 m And under…

Q: Use Trapezoidal Rule with number of sections (4) to calculate the double integral below 2 3 I =…

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Q: Find the general and particular solution that satisfy the boundary condition. (3x + y)dx – (x +…

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Q: Evaluate the line integral [(x + 7y)dx + (2x − 3y)dy along the curve C: x = 4 cost, y = 8 sint (0…

A: line integral

Q: Find the value of y(0.2) using fourth order Runge-Kutta's method from: dy -2.xy', y(0)=1. dx

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Q: 2 -πx²y. = The volume of a right circular cone of radius ï and height y is given by V 3 dy when x 4…

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

A: y=16-x2,  -1≤x≤1 Differentiating with respect to x, we get…

Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: 4. Given f(x, y) = arctan(x + 2y). Find the local linear approximation of f at (1,0) and use it to…

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Q: Suppose a function y = f(x) is so be revolved at x = e from point (a,b) to (c, d), what is the…

A: The surface area generated by revolving the curve y = f(x) between x = a and x= b  revolved about x-…

Q: The area of the surface generated by rotating the curve y = 1 = cos(3x), where 0 ≤ x ≤ , about the…

A: Let's find Area of surface,when rotated about x axis.

Q: 5. Find de for y = 3csc x + x2 dy On= -3ese(#)cot(2) + 1) dy = -3csc x)cot ( x 10 dx O 2) dy…

A: Given that: y=3cscx+5x2

Q: Q3) Evaluate triple integral S" dz dy dx. x-y

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Q: Set up an integral for the length of the curve. 5) y = x6, 0 s x s 1 A) V1 + 6x5 dx B) + 6x10 dx 1…

A: =&gt;ds=√(1+(dy/dx)^2 .dx

Q: If f(x, y) the total differential of f at (0, ) i 16e Cos x + 7 cot y, then the total differential…

A: Total differential