1) Evaluate the following iterated integrals. a) Lo Lo b) ff c) Explain why Fubini's theorem doesn't apply to these integrals? x-y (x+y)3 dydx x-y (x+y)3dxdy

Q: x+2 dx x2+4x-2

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Q: + 4x – 2) dx -1

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Q: 2x4 1+x² a) [: dx b) [ cos² cos² 2x dr

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Q: – x²y? x2 + y? f(x, y)

A: fx, y=-x2y2x2+y2 Now, z0=fa, b=f1, -2=-12-2212+-22=-45 Now partially differentiating fx,…

Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

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Q: Evaluate the integrals. (5 – 5t)i + 4vtj + 3 k dt -

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Q: dw V5 – e-2

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Q: For any a > 0, evaluate the integral ∞ fo 0 1 - cos(ax) x² dx.

A: We use differentiation under integral sign to solve this problem.

Q: dx (§5.7, Q28) Evaluate the indefinite integral: (x – 9)5"

A: step 2 complete solution

Q: (c) Let ɛ be a number so that 1 > e > 0. Explain why the integrals dx, dx x2 -1 can be computed…

A: For (c), Let ε be a number so that 1>ε>0. Now, we will show why ∫ε11x2dx,   ∫-1-ε1x2dx can be…

Q: b) Evaluate the integrals using substitution: (Hint: rewrite using algebra before determining u) X…

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Q: b) Integrate the above via 6ver the complex numbers! partial frachion deomposition X= - 6 b2-4ac X+2…

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