Evaluate the line integral along the curve C. [(x+3y)dx + (x-y)dy, C: x= 2cost, y = 4sint, 0≤ts- 05-2π O 3+2π 03-π 03-2π F|+ π 4

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A: A detailed solution is given below.

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A: The objective of the question is determine the derivative of the given function.

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A: A detailed solution is given below.

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A: To determine the volume of the region between y=x2 and x=y2; revolved about x=1.

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A: Note : according to our gauideline, i can solve oy first so please reroute the remaining question.…

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A: If the integral gives finite value , it means integral converges otherwise diverges.

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A: Please see the below picture for detailed solution.

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A: To find the domain and range for the function given below.y=x-2

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A: We know, ∫dx/x= ln|x| ln|a| - ln|b|= ln|a/b| n*ln|a|=ln|an|

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A: As per bartleby guidelines we only give first question answers.

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A: ddx9+9-x

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A: Answers of the all above question is

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A: According to Bartleby guidelines I can only answer the first question of the given problems

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A: We have to find the △h(e2x-1).

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A: Given, z=6ex2y3

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A: solution:-f(θ)=2cscθ+π4=2sinθ+π4sinθ+π4≠0θ+π4≠nπθ≠nπ-π4Domain: all real θθ≠nπ-π4,…

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A: Use vector concept

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A: Since the student has posted multiple questions and does not mention any specific question, so we…