Find the mass of a wire that lies along the curve r(t)= (t² – 8) j+2tk, 0≤t≤2, if the 3 density is 6= —t. 2 S8(x,y,z)ds= C (Type an exact answer, using radicals as needed.)

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Q: 2. Use Gauss' Lemma, to compute (²) = (-1)², μ = |aPn N, -6 (30). 31

A: We recall Gauss's Lemma and using Gauss Lemma we solve the problem.

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A: The given setThe augmented matrix

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A: We use the formula for centroid to solve this problem.

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A: We shall be using basic results from quadratic reciprocity for solving this problem.

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A: We use the Fourier transform to evaluate the following integral.∫−∞∞xsin⁡(2x)x2+9dx

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A: Given that Recall  the  formula  of Fourier  transform  of  Now,   [by  definition(1)]

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A: Euler method is given by:yn+1=yn+hf(tn,yn)

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