y' = 2 – 3xy; {-1

Q: /Find the area under the curve y = sin x cos 2x from x=0 to x =-

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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

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Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Use the Fundamental Theorem of Line Integrals to calculate exactly. F-6 sin(ox +)+ sin(6x )j along…

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Q: Find the area of the region that lies inside both curves

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Q: Evaluate the integral / (12x + 3y)dæ + (3x – y)dy along the parabolic arc y = x² from (0, 0) to (1,…

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Q: Evaluate the line integral J xe" dx +y sin y dy along the triangular path consisting of the line…

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Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy

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Q: Express the arc length of the curve y = x 4 between x = 2 and x = 6as an integral (but do not…

A: Given y=x4 between x=2 and x=6

Q: Sketch the region of integration. (Select the correct graph.) "In 3 dy dx In y y y

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Q: Use Green's theorem in order to compute the line integral £ (x – 3)³ dy – y³ dx where is the circle…

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Q: Plot a direction field and some integral curves for xy' - 2y = -1 (A) on the rectangular region {-1…

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Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Find the maximum and intlection points between X =0 and 2T tor the curve /2-s Sin X

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Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Find the path y = y(x) for which the integral 1. r2 VaVi+y(xdx is stationary.

A: The path y = y(x) for which the integral is stationary satisfies Euler’s equation given by,

Q: Find the area of the region between the curve y = 3 - x2 and the line y = -1 by integrating with…

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Q: sketch the region of integration and evaluate the integral.

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Q: Find the centroid of the region bounded by the given curves. y = 8 sin(5x), у 38 cos(5x), х-D0, х 3…

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: Calculate the area of the region bounded by: r = 3 cos(0),r = 3 sin(0) and the rays 0 = 0 and 0 =

A: r=3cos(θ)r=3sin(θ)θ=0  and θ=π4Area of the polar…

Q: express the length of the curve as an integral but do not evaluate it. r = sin3 θ, 0≤ θ ≤ 2π

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Q: Evaluate the line integral / (6x + 2y)dx + (x – 7y)dy along the 10 cos t, y in (0 <t: curve C: x =…

A: A detailed solution is given below.

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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Q: Find the area bounded by axes and line 7x + 5y = 35 using any differential strip

A: Explained  below...

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: Evaluate the integral (8 (8x+15y)dx + (27x - y)dy along the parabolic arc y = x² from (0,0) to…

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Q: (5)Obtain the integral curve for x 2+y = x passing through the point

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Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

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Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation!…

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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: 5. Find the area enclosed by the inner loop of the curve r = 1-3 sin 0

A: Area Between Functions With Integration: The interval of the inner loop of the given polar curve is…

Q: 9 Set up an integral for the length of the Curve, yこx,05x<ト

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Q: An area is bounded by the x^2+10y-1600 curve  and the -xaxis. Find the moment of inertia (in units4)…

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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: dl /x² + y² + 4

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Q: (5) Obtain the integral curve for dy +y cotx = e*cscx passing through the dx point (0, 0).

A: We have to solve the given differential equation

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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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: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Consider the curve defined by the equation y = 3x + 4x. Set up an integral that represents the…

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Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…