Let X,y EIR. Prove that if 21 x +35 y = 45 then x and y are not both integes.

Q: Suppose f(x, y, z) = (a) As an iterated integral, 1 x² + y² + z² and W is the bottom half of a…

A: Triple integral

Q: 1+x a) (-x² + 2y) dydx; 0. x2

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Q: Evaluate the double integral f(r, 0) dA. ' π/2 re dr de

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Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: Evaluate the double integral f(r, 8) dA. * T/2 (5 cos(8) r dr de T/2 Jo

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Q: use a computer algebra system to evaluate the triple iterated integral.

A: Using a calculator we get:

Q: x+y+xy)dydx 2J-1

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Q: Define f : [0, 1]→R by f(x) = x. •1 Use the definition of the integral to prove that 1 x dx |

A: Definite integral: An integral that contains the upper and lower limits then it is a definite…

Q: Evaluate the iterated integral | dydx. а. 2 b. 1 с. 0 d. 3 О а. O b. O d.

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Q: dz where C:|z – 2| = 0.2 (z – 2)³(z – 5) by using (a) Cauchy's integral formula

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Q: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

Q: Use the definition. that sinz •prove Z = UJZ %3D

A: Using definition of derivatives.

Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

Q: Evaluate the iterated integral. * Tt/2 r cos 0 dr de dz -1Jo

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Q: c) Evaluate | V In(z)dr by using integration by part.

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Q: Suppose that h is integrable and that h(r) dr = 0 and L h(r) dr = 6. Find .3 h(r) dr -/ h(u) du a.…

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Q: Find the double integral ∫∫R(2x^2−5y)dA, where R=[−1,2]×[1,3].

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Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) 4t-5 dt. If the integral does not…

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Q: Evaluate the integral. *T/2 csc t cot t dt 31.

A: 31. we have to evaluate the integral∫π6π2csc(t)cot(t)dt

Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

Q: 4 ∞ dy dx J I+ 4? 2. 00

A: To find the integration

Q: ex What is the integrable form of dr? e* – e° A 2 du B (u²– 1) ² du (u²– 1) ² du D (1-u²) ² du

A: In this question we have to find the Integrable form of the Integral.

Q: Evaluate the integral. л/2 csc(t) cot(t) dt T/4

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Q: Find all Integers a so that the area enclosed by the lines y=ax,y=0 and x + 2y-4=0 is a natural…

A: To find: All integers a so that area enclosed by the lines y=ax, y=0, and x + 2y-4=0 is a natural…

Q: Use the Fundamental Theorem of Calculus to evaluate the integral: 5/4 sin x dx. Jπ/2 C. A. - B. D.…

A: The objective of the question is evaluate definite integral using the fundamental theorem and choose…

Q: Use a computer algebra system to evaluate the iterated integral. V 25 - y2 y dz dx dy 25 - y2Jo

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Q: Evaluate the iterated integral. *T/4 4 - r rz dz dr d0 Jo Jo

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Q: Use the Fundamental Theorem of Calculus to evaluate (if it exists) where If the integral does not…

A: Solution

Q: 1/ Math

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Q: 1- Assume that x, y € R and z = x + iy € C .Calculate the following integrals using the given…

A: a) Given ∫0∞lnx1+x2dx ∫0∞lnx1+x2dx=12∫-∞∞lnx x-ix+idx=122πi Resi=πiln i2i=π2ln i=π2ln1+π2 i=π20+π2…

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Evaluate So y? exy dA, where D 'is bounded by you, yit, x

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Q: Evaluate the integral: 2+u du a) b) / e"V1+ ev dy

A: Evaluate: i ∫252+u3uduii ∫ey1+eydy

Q: evaluate the contour integral z^2 -z^4/z-1)cos(z)where c:|z|=4

A: Introduction: Cauchy's integral formula is very significant in complex analysis. It helps to…

Q: Evaluate the integral ff, (x + y) dA, where R = {(x,y): 1<x² + y² < 4, x< 0}. %3D

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Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: The suitable substitution to evaluate the integral [V tan (2x) dx is cos (2x) O u= sec(2x) u =…

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Q: Evaluate the iterated integral. T/4 '3 '3-r rz dz dr de

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Q: Find the integrals. a) R= %3D R.

A: First we have to plot region of integration.

Q: Evaluate the iterated integral. '2 (z (x + z 19xz dy dx dz /o Jo Jo

A: GIVEN DATA : Iterated Integral ∫02∫0z∫0x+z19xz dy dx dz Let the given integral is I=∫02∫0z∫0x+z19xz…

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

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Q: Evaluate the line integral [F-dš where F = 2xyi + (x – y')j and C is (a) y =x from (0,0) to %3D…

A: For the solution follow the next steps.

Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: Prove,J w' Sin wx du %3D COSZ 2

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Q: Evaluate the iterated integral 3r'y drdy

A: