S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

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

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Q: dx 1s+ kıl35-x) +kaly-x) dy %3D dt k, , k. k3 are Con Stants.

A: Given system is dxdt=15+k135-x+k2y-xdydt=k2x-y+k335-y Here, 1k1=5⇒k1=151k2=10⇒k2=1101k3=5⇒k3=15 So,…

Q: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: Find the partial integral. + 3y?) dy t.

A: Given that a  integration and we solve this integration by using general formulas of integration. We…

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: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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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: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: dv Integrate ду 1 partially with respect to y. II

A: To partially integrate the given function with respect to y, implies x will be treated as a constant

Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: 3. If w = e3x-2y cos 4z where x = Int , y = In (t² + 1), z = t3, aw at t = 1? at what is the value…

A: Consider the following equation: w=e3x-2ycos4z Substitute x=lnt, y=lnt2+1 and z=t3 in the above…

Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

Q: (b) Calculate fe" con(r2) dz using integration by parts as many times as necessary.

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Q: Evaluate f S S 4.x² + 4y² + 4z² dV, where R is the hemisphere centered at the origin, R having…

A: Given that:- ∫∫∫R 4x2+4y2+4z2 dv where R is thehemisphere centered at the origine havingradius 2.…

Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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Q: dy -y ze°Cos(E) dt y le) =0 1+らine

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Q: Reverse order, then integrate SaE ) dydx. Vx \1+

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Q: Evaluate (2х — у) dx + (х + 3у) dy. C: elliptic path x = 4sin(t), y = 3cos(t), from (0, 3) to (4, 0)

A: Line integral

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: Evaluate the double integral : 9. dy dx 0, 22

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Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

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: Find the value of the line integral 6xy dx + (3x² + 4y2)dy, where C is an ellipse 16 + = 1 from (4,…

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

A: Solution is below

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: Solve the problem using convolution integral   y′′ + 2y′ + 2y = f(t), y(0) = 0, y′(0) = 0

A: Convolution Integral: Let f(t) and g(t) be defined in [0,∞). Then, the convolution of f(t) and g(t),…

Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: Find y', where t (a) y = Jo dt VE2 +1 (b) y /t² +t+1 dt 1 • sin²3x (c) y = | 1 dt t2 +1 Cos x

A: The given function is: y=∫cos xsin2(3x) 1t2+1 dt

Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

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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: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: What is the value of the line integral ∫AB xy dx defined by the line y = x +2 and it is along the…

A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: cos(x + y) dx +(3y² + 2y + cos(x + y))dy = 0, with the boundary condition of y(1) = -2.

A: Here given differential equation as cosx+ydx+3y2+2y+cosx+ydy=0This equation is of the form…

Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

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Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Evaluate. (use C for aonstant of intgration) dx 2 X "- 3

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Q: Q3/ Evaluate 2 vsinx dx, using i- Trapezoidal rule ii- Simpson's 3/8 rule Ans. 1.1615

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Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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Q: e for (2x + 1) cos(x) dx. 14. Use integration by parts to evaluate

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: does not exist. (b) If u = x cos y+ye", where x=s+2r and y = st , prove that ди ди dt = (s – 21) (x²…

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Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Ssinx Losxdx X. a) vse u=coS X Esie to evalvale %3D b) Vre V=Sinx to e valvate %3D

A: