3 4 dx . (5+2x)' 3. Evaluate

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A: Integrate by parts.

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A:

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A: Green's theorem states that for  counterclockwise direction∮CPdx+Qdy=∬R∂P∂y-∂Q∂xdxdy

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A: To find r'(t), r"(t), r'(t).r"(t), r'(t)×r"(t).

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A: The given integral,     ∫x2lnx dx

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A: Solved below.

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Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

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A: Just use the trigonometrical substitution to make integral easy and then solved it.

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral

A: Our Aim is to identify the correct step to evaluate ∫x2 ln (x) dx to yieldthe correct integral.

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A: We have to check

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A: In this question , we can find the given line integral.

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A: Given: x=6