Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

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: Evaluate the triple integral. 3x dV, where E = {(x, y, z) I 0 s y s 2, 0sxs V4- y², 0 s z s 2y}

A: Given region is E=x,y,z/0≤y≤2,0≤x≤4−y2,0≤z≤2y We have to evaluate the triple integral ∭E3xdV in…

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

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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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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: DE with Integrable Combination (v + xy + 1)dx + (x² + xy² + 2y)dy= 0.

A: We will find out the required solution.

Q: V24z – 2z3 dz dy dæ, by changing the order of integration to dæ dy dz.

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Q: Sketch the region of integration. rIn(x) f(x, y) dy dx

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Q: y = Vx, 1 SxS 8 (a) Integrate with respect to x. -(9) )* (b) Integrate with respect to y. 2 2nyV1+…

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Q: Find dy at (x, y) = (TT, T) for sin (xty) = 2x-ay %3D dx

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Q: dt u = xy + y z tzx x = tcost, y = tsint, z=t at t = a 4

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Q: Sketch the region of integration and change the order of integration. T/2 cos x f(x, y) dy dx

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Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

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Q: ƏF Find at (x, y) = (T, 1) if f (x,y) = cos vt dt. cos yt dt. ww

A: given,          fx,y=∫0x2ycostdt

Q: The reverse order of the integration J. Jy f(x,y)dxdy is A) SF f(x, y)dydx B) f, J fcx,y)dydx C) S,…

A: Here we have to change the order of integration.

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

A: We have to solve the initial value problem cos(x+y)dx+(3y2+2y+cos(x+y))dy=0 with the boundary…

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: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

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Q: Set up an iterated triple integral equal to √√3 S√ SO 3-x² x²+y² 3 2- 4-x²-y² using: a. Cylindrical…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Find the total differential. z = x cos(y) – y cos(x) dz =

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Q: Evaluate the triple integral. -{x, v. 2) 1 0 s x s 1,0 s ys x, x szs 2x} 19yz cos(16x5) dV, where E…

A: According to the given information, it is required to evaluate the triple integral.

Q: Compute 6. da dy dz x²+y² + z² where V = {(x, y, z) E R³ : 4 0, y > 0}. Sketch the solid.

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Q: Evaluate the iterated integral. V9-y y dx dy V9-y y dx dy = i

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z²…

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

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Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

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

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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: Vy+I ydx dy -1 -Vy+1

A: Let's find.

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: Verify the condition of integrability for the given total differential equatior (3x*y2 – e*z)dx +…

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Q: Change the order of integration in the ihtegirul dx 1=, dy 1+Vi=y 1-VI-y (x-2x+y-3)² and hence…

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Q: Evaluate the iterated integral. IIT*+y+z) dx dz dy

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Q: Sketch the region of integration. (Select the correct graph.) dy dx y y 1 1

A: Order of change of integrals

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: Find the partial integral. Y dy

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: Obtain tne general voluti on' 1. (xy + x) dx (x*y* + x * + y² + ) 2 2 %3D X cos²y dx =tany dy 2 Q.…

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Q: Sketch the reglon R of integration and switch the order of Integration. 16 - y2 f(x, y) dy dx -2 4…

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Q: Supply the missing integrand and limits of integration. 5 a) S S,2 6x²y dxdy = dy -5 сx/2 b) S S²…

A: We have to find the missing integrand and limits of given integration.

Q: Consider z = x² + 3y², where x = sin t and y = cos t. Calculate dz / dt.

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Q: Evaluate the triple integral. {x, y, z) | 0 s y s 2, 0 sxs 4- y², 0 sz s Sy 6x dV, where E =

A: From the given problem:   ∫∫∫E6xdV   And region:   0≤y≤20≤x≤4-y20≤z≤5y   So, we can write as:…

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: y³ Vy² + 4 dy Let u = y? 2

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Q: Compute on your paper, showing all work: dy dx (i) = x + y (ii) y = xy + 2x² at the point (-1, 1)…

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Q: Sketch the region of integration. sin x dx dy 1.5 y. 0.5 y 3 -05 21 -1 -1.5 1- -1 1 3. 4. 4 0.5 2.…

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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

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