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A: To evaluate the given integral.
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A: See the attachment
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A: A detailed solution is given below.
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A: topic - Area bounded by curves
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Q: 1. Evaluate the double integral of x+ 2y whose region of integration is represented below. y = 1+ x…
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Q: 2] evaluate the Cauchy principal value of the given improper integral. 1 dx x²- 6x + 25 (x² + 1)2 dx…
A: Note: Our guidelines we are supposed to answer only one question. Kindly repost other question as…
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- Show that A' y= V yk+rLet F = 10xe³i+ 5x²e³ j and Ğ = 10(x − y)i + 5(x + y) j. Let C' be the path consisting of lines from (0, 0) to (7,0) to (7, 3) to (0, 0). Find each of the following integrals exactly: (a) F. dr = 0 (b) fc G. dr = 735 220. Use integration tables to find J coox 7sinx + 5sinx + 4 dx
- d) S x sin (4x) dx y=- 1. (3,4) Set Up only Area bounded between the lines 2x+y=-2 X-ye-1 (-1,0) 7x-y=17 and 7x-y= 17 2 x +y= -2 a) dx b) ag DELLLet F=6xe+3x²ej and G = 6(xy)+3(x+y). Let C be the path consisting of lines from (0,0) to (5,0) to (5, 4) to (0, 0). Find each of the following integrals exactly: (a) So-dr- . (b) fc G.dr=Consider the integral , 5y + 5x = 25, y - 4x = 0, and y - 4x = -25. (5y + 5a) dA where R is the parallelogram bounded by the lines 5y + 5z = 0 Compute the Jacobian corresponding to the change of variables u = 5y + 5x and v=y- 4x. The integral evaluates to > Next Question
- 2. Find the INTEGRATING FACTOR (I.F.) by INSPECTION Please strictly use method of INSPECTION ONLYUsing the substitution =vy, dx=vdy + ydv _ the DE (1+2e*") dx + 2e* (1--)dy=0 reduces to the separable DE A (1+2e")dv + 2e" (1 – v) dy =0 B (v+4ve"+2e")dy + y(1+")dv=0 © (v+2e")dy + y(1+2e")dv=0 v(1+2e")dy + y(1+2e")dv=0Differentiate: 1. y''' - 4y'' + y' + 6y = 0 2. yIV + 16y = 0
- In integrating the function fx In 5x dx using integration by parts, what would you choose for your u? u = x3 O Option 1 u = In 5x Option 2 u = Option 3 x+ u = Option 42. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment from (2, 1) to (-1,1), followed by the piece of y = x² from (-1,1) to (0,0). Also, let F = (-1,2y?). a) Find F-Ťds F-Ť ds by integrating F over each piece of C and adding the results. b) Find F.Ť ds by first converting it to a double integral using Greene's Theorem.1. Compute the value of constant (C) by solving the given DE using integrable combination. Let x=3, y=1 2y^2(xdx+ydy)=1(ydx-xdy) 2.Compute the value of constant (C) by solving the given DE using integrable combination. Let x= 1, y=2 xdy+ydx=6xdx