Please solve this question correctly in 30 minutes and get the thumbs up please show neat and clean work.please solve both parts Question 4: Let E be the solid region of integration ofLIL(b)15(x + y) dy dz daSketch each of the following:the solid Ethe projection of E onto the xy-planethe projection of E onto the yz-planethe projection of E onto the xz-planeSet up (but do not evaluate) the given integral in the order da dy dz. Show your work!

Answered: Image /qna-images/answer/28153cfd-e89a-41c4-a536-6d4acae17014.jpg

Answered: (a Question 4: Let E be the solid…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Let I= · S₁² S₁ = √² + y² dx dy +_ (a) Sketch the region of integration. Y +√√√²+₁ I√² + y² dr dy. (b) Rewrite I as an iterated integral using the order dy dr. (c) Describe the region of integration in polar coordinates. Show all your work! Complete the blank spaces: D = {(r,0)| ≤r≤ (d) Set up the iterated integral I in polar coordinates. (Do NOT evaluate the integral). < 0 <
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Q.2/ Change the following Cartesian integral into an equivalent polar integral and evaluate it: 1-(x-1)2 x2y 3 dy dx (x2+y2)
Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is the triangle with vertices (0,0), (9,0), and (0,5) with counterclockwise orientation Poxy dx + 4x°y° dy= (Type an exact answer.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear All 14 2 Type here to search 近

Verify Green's Theorem for [(by − 3y² + x) dx + yz³ dy - where C' is a triangle with vertices (0,0), (1,3), and (1,5) traced out counter-clockwise by (a) computing the line integral directly and (b) using Green's Theorem to compute the integral.
Q6 (a) Transform the integral to polar coordinates and calculate the integral. و تا 1 dxdy Vi+x? + y? Apply the triple integration to calculate the volume of the solid G that is bounded above the hemisphere (b) /25-x - y , below by the xy-plane Z = and laterally by the cylindrical x + y² =9. Given the function, f(x, y)=2x² – y' –2xy Find all the critical points of function f(x,y) (c) (i) Activate Windows Differential each critical point whether as a local maximum, local minimum or saddle point (ii) Go to Settings to activate
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X Z=1 R N -x=ln4 Y Curve C x=ln2 Consider a structure D with a curved solar panel wall that is moulded to a curve C, as shown in Figure 2. D occupies the region below the surface z = f(x, y) = 1 and above the region R on the xy-plane. R is bounded by the planes y=0, x=In2, x=In4 and the curve C which is parametrised by x = ln(t + 2), y = (+1)' t>-1 (a) Write down an expression for the arc length of C between its intersection points with x=ln4 and In2 (blue dots in Figure 2). Leave the expression in integral form. (b) Express the equation for the curve C in y=f(x) form.
-V2/2 4-x I 2 Vx2 + y² + 3 dy dx + 2 Vx2 + y² + 3 dy dx -V2 V2/2 J VI-x² Rewrite as an iterated double integral in polar coordinates and evaluate.
Q3)Verify the Greens theorem to the integral f(2x*y-x)dy+(2y'x-y)dx where C is atriangle its vertices (0,0),(2,0),(2,2).

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