1. Evaluate the integral 2 8x cos y dy dx y – 4 by reversing the order of integration.

Q: For any fixed x in the interval (0, 1] carry out the substitution cos 0 = y + (y² – 1) in the…

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Q: -3 Evaluate the triple integral ²³ sin(y²) dz dx dy.

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Q: Evaluate the iterated integral below. π T/4 A lago S. 0 1 y cos (x) dy dx

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Q: Evaluate the iterated integral. 2y (2 + 4x² + 8y²) dx dy 0 Jy

A: To evaluate:∫02∫y2y2+4x2+8y2dxdy

Q: 4. (a) Evaluate the integral (b) Show that 0 1 S [ f*cos(y²) dy da 0 Ste 1 + ex+y dx dy 4.

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Q: #1. Evaluate the iterated integrals (a) || (6x?y+4x - y) dx dy -2 (b) y2 x²y dxdy

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Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

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Q: Let I = [ -1 y+x y-19y+xª dxdy. By reversing the order of integration of I, we get: Osysx^2+1…

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Q: valuate the iterated integral below. π/4 1 St. + S² = 0 0 y cos (x) dy dx

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Q: Evaluate the iterated integral. 2y (10 + 2x2 + 6y²) dx dy 0 Jy

A: The given integral is: I=∫02∫y2y 10+2x2+6y2 dx dy

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

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Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

A: Since, you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the iterated integral. 8 3 (x + y²) dx dy -1/1

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Q: 1. Evaluate the following integrals (mixture of integration techniques). (a) /e's y² +8y- 3 sin 0 de…

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Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy

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Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

Q: Evaluate each of the following partial integrals. 1. 2 co e*sinydxdy 2. (x + 2xy - 3y?)dydx II. 2e…

A: It is partial integral

Q: Evaluate the iterated integral. /2 x. 4 cos (x + y + z) dz dx dy

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Q: (a) Calculate the iterated integral 3 7/2 SS(v+y° cos x)dx dy -3 0

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Q: Evaluate the iterated integral 2y dy dx 2 x +1

A: on solving this we get the

Q: y3 (b) Solve the integral . (cx – y)dx + (2x + y)dy along the curves x = from (0,0) to (1,1)

A: The given problem is to evaluate the given contour path integral over given path x=y3.

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-2

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Q: Evaluate the iterated integral.

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Q: Evaluate the triple integral ∫ 2 to 0 ∫ 2x to 0   ∫ ln x to 0 xe^−y dy dx dz

A: The given integral can be written as: I=∫20∫2x0∫lnx0xe-ydydxdz…

Q: T "cos(x²)dxdy? What is the reversed order of integration of 'y a. I T cos(x²)dydx ST"cos(x²)dydx O"…

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Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: Compute the following integrals. 1 t3 (a) dt. Jo V4+ t² (b) e6x cos (3e2) dx. (Hint: you might need…

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Q: Reverse the order of integration in the following integral. cos (x.у) dx dy

A: The given double integration is: ∫05∫0cos-1y5f(x,y)dxdy The limit of x in the given integral is…

Q: Evaluate the iterated integral. 2 3 4 (x² + y² + z² ) dx dy dz -2 0 0

A: ∫-22∫03∫04x2+y2+z2dxdydz

Q: Question included in image

A: The given integral is,

Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: Evaluate the iterated integral. 5 cos(r + y +:) dz dx dy

A: We know that integration of sinx is -cosx + c  and integration of cosx is sinx + c.       Here i…

Q: Evaluate the double integral : 2 e2y+z dy dx 0. 0.

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Q: Evaluate the iterated integral. π/4 ** ['y cos(x) dy dx

A: Please see the below picture for detailed solution.

Q: 13. compute the integral // e10(x-y)²+8zy dædy over the ellipse & := {(x, y) ; 5x² + 5y² < 6xy+ 1}.…

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Q: (b ) [. SS. 1 dx dy dz xyz

A: Given ∫1e∫1e∫1e1xyzdx dy dz

Q: 3. Evaluate Sy In(1+ y) dy using integration by algebraic substitution.

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Q: Evaluate the iterated double integral: x+4 sin (y³ – 3y?) dy d.x - x+4

A: Let's find.

Q: II cos(s5) dt ds

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Q: ]] x² + y² 1+ y² dx dy

A: We have to evaluate the integral ∬x2+y21+y2dxdy, Where D:0≤x≤y≤1 Here, limit of x is 0≤x≤y And limit…

Q: 1. Evaluate the following integrals (mixture of integration techniques). sin' 0 do cos O y² +8y- 3…

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Q: 25 2 8 5 cos (x²) 4Vz Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Consider the provided question, We have to find the integral ∫025∫02∫4y85cosx24zdxdydz by changing…

Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: (In =)"dz = z(lnz)" – n (In =)*- da Use integration by parts to establish the reduction formula: %3D…

A: Formula given is  ∫(lnx)ndx=x(lnx)n-n∫(lnx)n-1dx Integration by parts formula is  ∫udv=uv-∫vdu we…

Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy -3Jo

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Q: Evaluate the iterated integral. 6. I (8x - 2y) dy dx | 1

A: Given: ∫19∫0x8x-2ydydx

Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

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Q: Evaluate the iterated integral. (x² – y²) dy dx J-4

A: Given the double integrationI=∫−11∫−44(x2−y2)dydx

Q: Evaluate the iterated integral. 16 - y2 4 (x + y) dx dy

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