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

Q: Find LOVE LOVE 0 0 [Trysin(x² + y²) dady

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Q: b) I =f- x(1+(In x))

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Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

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Q: موضوع الدرس: Find the sewera (BY COS X + 4X +2x S * 6 ution of Jdx + (3 $ inx+3) dy ap

A: The given differential equation is         (3ycos x + 4xex + 2x2ex)dx + (3sin x + 3)dy = 0 We can…

Q: Find Cn in terms of C0 when: 1. Cn = Cn-1/(3n2 + 4n): (Note that C1 = C0/7, C2 = C0/140, C3 =…

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Q: Evaluate: L(e* -3t * sinh 7t).

A: Given: Le-3tsinh7t

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: Verify that det(AB) = det(A) det(B) for the following:

A: Given: The given matrices are A=1-23-231010 and B=1023-25213. First, find the determinant of A and…

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Is Q closed over multiplication? (Y/N)

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Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: 6. Use a substitution to find S (x* + 1)" z³dx.

A: Here we use substitution we find∫x4+111x3dxHere we substitute x4+1=du…

Q: What is y' of y= 7√x 3√x ? A B C D 21√³ (In 7 + ln 3) (In 4) 21√x √x 21√ In 10 2√x 3 In ( - ) 21 V ²…

A: We have to find the point on paraboa y=-x2+4 whose tangent line is parallel with y=3x+5Parallel line…

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: 49

A: ln4te6t

Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

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Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

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Q: 46) Evaluate V(3r + 1)dx 2(3r+1)7 O s(3z+1) 2 O 2(3z+1)7 +c 3 O D(3r+1)1 + c 2

A: We have to solve the given integration

Q: Prove the follawing identities. 4-V. 4- V = AV (a) (b) M8 = A/1+ 4) (1+ A)" 2. (C) 4/f = I for Afn-…

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Q: nd y axsis labelled ?

A: Morphospecies on A Morphospecies on B Morphospecies on C 7 13 3 7 9 4 2 4 4 4 4 2 11 14 10…

Q: Suppose v = 3i − 2j + k and b = 2i - 6j + 3k. (a) Find the vector component of v along b this is…

A: To find the vector component of vector v along vector b (proj_b(v)), you can use the projection…

Q: Compute a (х + 2) dx. O x3 + x² + C O x² (x² + 2x)+C x2 + 2x ) + C 2 - + C 2 + x2 + C 3

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Q: Evaluate L{3 (r² – 1) sin (21) + 7e cosh (41)}

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Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: (zin z + 5)dz

A: The given integral is [xlnx+5] limit from 1 to 3.