Find the area of the region bounded by the curves x=y3 and y=x2.

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A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: Given  u=-2i+4j-5k & v=2i-4j+5k

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A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: Find the centroid of the given region. y = 2-x? y = x A (3/22,45/61) В) (5,15) c) (5/14,38/35)…

A: Centroid is x¯,y¯ , where, x¯ = 1A∫ab xfx-gx dx  and y¯ = 1A∫ab 12 fx2-gx2 dxand A = ∫ab f(x)-g(x)…

Q: 5. For each integral, state u, du, dv and v you would use to Integrate by parts a) fln(1+x) dx…

A: These integrals are solved integration by parts.

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A: Solving the problem by finding the correct answer.

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Q: n and fractions where needed.)

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A: We need to find the solution for the given  integral by trigonometric substitution.

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Q: 10. Consider the system of equations X, - 2x, + 3x, = 1 2х, — Зх, — 2х, 3 3 X, - x, - 5x, = 2 a.…

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Q: 3. Suppose that the revenue in selling x tables is equal to 200x – 0.25x2 dollars, and producing a…

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A: Let's find.

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