Apply Green's Theorem to evaluate the integral. $(4y + x) +x)dx + (y + x)dy C: The circle (x-3)² + (y-2)² = 3

Q: 7) Find the area under the parabola y = x² – 2x +2, above the x-axis and between x = 0 and x = 1.

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Q: 2. Find the area of the plane figure bounded by the curves. Plot the graphs of the given functions,…

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Q: f(x) = √√/x = -²x³12 about the x-axis for 1 ≤ x ≤ 3. .3/2

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Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: SHOW COMPLETE SOLUTION. PLEASE MAKE THE SOLUTION/HANDWRITING CLEAR.   THANKYOU!

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Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: Find all points where the parabola y = 9 - x² 1 intersects the line y = zx+6. 2

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Q: ƒ(x) = √√x - 12/1x²³/2 about the x-axis for 1 ≤ x ≤ 3. 3

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Q: 1. Let F = (vi-x)/(x² + y²), evaluate § ♬ dr, where C is circle (x − 1)² + (y − 1)² = r² with 0 <r…

A: We are given that          F = (y i - x j)/(x2 + y2)   Now, r = x i + y j       =&gt; dr = dx i + dy…

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: ort er 2x² + 2y² + 4x + 8y + 8 = 0 is the equation of a circle with center (h, k) and radius r for:…

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Q: Usefe x dy - y dx to compute the area of the ellipse ()² + ()² = 2 = 1. (Use symbolic notation and…

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