If C is the line segment from (1, 5) to, (0,0), find the value of the line integral: So(4y? i + 4x j) · dĩ =

Q: Q5: A) Evaluate the following integral : S(z? – z-2)² + 4 dz B) Find the slope of the line tangent…

A: To evaluate the integral, the function z2-z-22+4 has to be first simplified. Now, z-2 can be…

Q: Find the following integral: i) Sdx S dx 3x2+1 ii) Sx/(x+1) dx

A: We have to find the integral  ∫x3x2+1 dx ∫xx+1 dx

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge…

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Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: 1 Which integration technique should be used to find dæ? x2 +3x + 2

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Q: dr. +37-10z

A: We have to evaluate the given integral.

Q: Find ∂z/∂t if z = sin(5x3-3y2), x = 2s2+t2, y = 2st3. Write in terms of the two independent…

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Q: Evaluate the iterated integral I = SoS"(24y + 2) dady

A: Answer for the integral is : 14

Q: Find the value of integral 2+1 (y² +ix) dz

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Q: Find the integrating factor to make the following ODE exact У(2ху + е*)ӑx -е*dy %3D0.

A: Let's first check if the given differential equation is exact or not!   For the given differential…

Q: find the integrate(v . dr) of the following case:

A: To evaluate the line integral ∫C​v⋅dr, where v=(2xy,x2+2yz,1+y2) and C is the circle x2+y2=1 in the…

Q: Differentiate r(t) = 5t cos t.

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