Verify Green's Theorem by evaluating both integrals ƏN Ly? dx + x² dy dA ду - %D ax For the given path. C: boundary of the region lying between the graphs of y = x and y = x2 y? dx + x² dy %D ƏN ƏM dA = ay - Əx

Q: Consider the area between the graphs x + y = 15 and x + 5 = y². This area can be computed as a…

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Q: Let f(x, y) and h(x) differ an tiable functions are given such that f f(x,y) dy = h(x) and Sh(x) dx…

A: and id A , A/2 , 2A , 3A represent the area of the regions.To Find:

Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

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Q: Evaluate the integral. 5x а. (25x²-10x +198)+c 125 Ob. (25x²+10x-202)+c 125 e -(25x²– 10x - 201)+ c…

A: The given integral is ∫x2-8e5xdx. Here we use the integration by parts formula:…

Q: Find the complete integral of 1 dz z dx 1 dz z dx2 1 dz = x1 X2 X3. z dxz %3D

A: Given 1z∂z∂x11z∂z∂x21z∂z∂x3=x1x2x3. Find the complete integral using the Jacobi method.

Q: Let o (x +e*siny) dx + (x +e* cos y)dy be the line integral on the boundary of the triangle enclosed…

A: We will find out the required value.

Q: What should be A for the path independent of (2,4) 2Ay – x dy. y? XY + A (1,2) over evaluate the…

A: Consider the provide integral,

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Find the area A of the region that is bounded between the curve f(x)=ex−1−6 and the line g(x)=−2x−3…

A: Given that the region that is bounded between the curve                                  and the…

Q: Verify Green's Theorem by evaluating both integrals v? dx + x? dy = . dA дх ду for the given path.…

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Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute the polor integral…

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Q: √ y² dx + x² dy = √₂ R C for the given path. C: boundary of the region I y² dx + x² dy 2 =

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Q: Let R be the region bounded by the curves y² = 2² + 1 and y² = ²-1 and the lines y=1-r and y =5-2.…

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Q: 11. Let D be the triangular region bounded by the lines y = 1, y = 2x and y = -x. Evaluate the…

A: Given D be triangular region bounded by y=1,y=2x,y=-x.

Q: Set up an integral for the length of the curve. y=√₁-x²₁ - sxs ² 1/4 -1/4 5-4x4 4(1-x4) 1/4 -1/4 dx…

A: Topic- Length of a curve we are given, y=1-x4,-14≤x≤14Length of curve f(x) over a≤x≤b…

Q: The line integral x dy – y dx Jc x2 + y? is independent of path.

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: Determine the area of the region between the parabola y = x and the line y = 2 x for the domain 0≤x≤…

A: Given y = x2y = 2 - x 0 ≤ x ≤ 2

Q: Find the area bounded by the curve y = x² and y = x+ WRITE THE GIVEN AND DETAILED SOLUTION

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Q: Let f(x,y) and h(x) differan tiable functions are given such that f(x,y) dy = h(x) and h(x) dx = 24.…

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Q: Use integration by parts to evaluate the following integral: Sx²e2x dx xe2x. e2x + C 8 | 4 xe2x + 2…

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Q: 3.x - I +6 dx Evaluate the integral: 2x x'+F - 3Inx+C A. r'+ + 3ln.x +C B. 2x - + |x + Inx + C D.…

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Q: y 3- 2- y(x) = Vx y(x) = -x+ 6 1- 2 3 5

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