Q3/ 2. Evaluate the integral by using polar coordinate for: 1. Compute 1 1-x2 x I (x2 + y?)dz dy dx -3 +r3 -1 00

Q: 4] [2M] Evaluate the iterated integral o So V sin(x2 + y? )dx dy by converting to polar coordinates.

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Q: ● Evaluate the following integrals: 4 Convert this Cartesian equation (x² + y²)²_9(x² - y²) = 0 to…

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Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…

A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx,  such that , the region is…

Q: 1.5 3-y QI) Evaluate the integral dx dy using polar coordinate

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Q: 63; Evaluate the întegral +3 dx + 6xy dy where Cay Curve Joininy (t, -) to (16, I),

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Q: b) Evaluate the integral by converting in polar coordinates [T 13 dy dr

A: (1) tan−1⁡(x)=cot−1⁡(1/x)(2) tan−1⁡(x)+cot−1⁡(x)=π/2 (3) 1/sin⁡(x)=csc⁡(x) .

Q: Evaluate the integral 18x dx. 64-x2 A 114 tan-) - 9x/64-x² + c 576 tan-) - 9x64-x + C 114 sin-) -…

A: To calculate the integral

Q: S(cos 3x + sin 7x)² dx

A: Here, when we solve this integration it becomes separate integration of trigonometric term and…

Q: Evaluate the complex integral rx+yi [*** az (ebz² +c) dz v if a = 5.7, b = 0.5, c = 3, v = 4, x = 1…

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Q: dy dz - to polar coordinates and evaluate it (use t for 8): With a = and d = fo S, dy da = dr dt = .…

A: To find :∫08∫-xxdy dx using polar coordinates Here y varies from -x to x as x varies from 0 to 8. In…

Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: 1/2 VI (Iy xy <p p xp

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Q: Q.1) Use the polar integral to evaluate 2 dydr 71+ Vr2 + y?

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Q: 7. Evaluate sizda by r (a) manipulating the integrand. (b) making a substitution. 88

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Q: Q.2/ Change the following Cartesian integral into an equivalent polar integral and evaluate it:…

A: We have to evaluate the given rectangular integral which has rectangular coordinates by changing…

Q: Use Stokes' theorem to solve ∮[(3x + 4y)dx + (2x + 3y2)dy] around the circle x2 + y2 = 4

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Q: The function B(a, B) is defined by a-'(1 – y)"-'dy. (a) Letting y = sin² 0 show that B(a, B) = 2…

A: Given  Bα,β=∫01yα-11-yβ-1 dy

Q: (1 point) Evaluate the iterated integral by converting to polar coordinates. NOTE: When typing your…

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Q: Use Green's Theorem to evaluate(¹-28) O-96 O-75 O 105 -2y) de- (62-4ry") dy where C' is shown below

A: We want to calculate the integral ∫Cy4-2ydx-6x-4xy3dy

Q: 2. Rewrite the iterated integral f(a, y, 2)dz dy dz in the order of -√1-z Jo (a) dz dy dr; (b) dr dz…

A: The given integral is, ∫01∫-1-x0∫0y2f(x,y,z)dzdydx. we have to write the iterated integral in the…

Q: EXAMPLE 3 Evaluate fE Vx + z'dv, where E is the region bounded by the paraboloid y = x + z and the…

A: To evaluate the below triple integral. ∫∫∫Ex2+z2dV Here E is the region bounded by the paraboloid…

Q: QI) Evaluate the integral dx dy using polar coordinate

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