Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C: square with vertices (0, 0), (6, 0), (6, 6), (0, 6) v? dx + x² dy = ON dA = ду

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A: The given integral,            ∫-55x2-x-6dx

Q: 55-58 Use the properties of integrals to verify the inequality without evaluating the integrals. 55.…

A: Let's find.

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A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

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Q: 27. | (u + 2)(u - 3) du 2+x 29.

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Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}cS,

A: Explanation of the answer is as follows

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A: Given :f=x3-y3

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Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: 5² - 13 ニ

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A: We have to find the volume by shell method.

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Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

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Q: A torus formed by revolving the region bounded by the circle x2 + y2 = 49 about the line x = 8 (see…

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Q: .

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Q: Use cylindrical or spherical coordinates to evaluate the integral. 2 cVA-y? cv8-x?_y² z?dzdxdy. A…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 5…

A: To evaluate: ∮C5y2dx+5x2dy Let, L=5y2& M=5x2⇒∂L∂y=10y, ∂M∂x=10x

Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.

Q: Current Attempt in Progress Sketch the curve by eliminating the parameter, and indicate the…

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Q: Evaluate the iterated integral. 4ze dy dx dz

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A: Option (B) is correct

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A: Trigonometry

Q: Sketch the region of integration. (Select the correct graph.) rIn 6 6 dy dx In y y y 61 6 4 3 2 1 4…

A: Area

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Q: sine "/2 Evaluate the iterated integrals r cos e dr de A 1/6 1/2 11/9

A: Explanation of the answer is as follows