(a) Compute the multiple integrals of (i) V4-z2 1 xy dxdydz (11) SS, (8 – x² – y²)dA, where R = {(x, y) = -1

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A: Value of the giveen integral is

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A: We will evaluate the given integral in this question.

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Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

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Q: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

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A: given , integral ∫∫∫xy+z2dV  where E=x,y,z:0≤x≤2,0≤y≤1,0≤z≤3 claim- to evaluate the integral

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A: Consider a function f(x, y) defined at every point of the 2-dimensional finite region A Divide A…

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

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A: Given,           ∫abfxdx=∫-28fxdx+∫810fxdx-∫-25fxdx

Q: 1. Reverse the order of integration on the following double integral. f(x,y) dy dx A. y) dx dy B. y)…

A: Given: ∫14∫1xf(x, y) dydx

Q: In 2 2 Change order of integration in iterated integral S S f(x, y) dy dx. ez

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Q: 1)Calculate the following double integrals. (y + xy-2)dA, where R = {(x, y) E R²/ 0 < x < 2, 1 < y <…

A: Solution:

Q: 1. Sketch the region corresponding to the double integral rx+2 dy dx x2 and reverse the order of…

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: 6. f(x)dz = f(t)dt, If what are the bounds of integration for the first integral? = and b =

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Q: Q1/Evaluate the integral: -За (2Vах dy dx x2 0, 4a by changing the order of integration.

A: We have to solve given problem:

Q: 4) Evaluate the following integrals: a) (z² + 1)ey2 dx dz dy , R = [0, y] x [0,24] x [0, ln 12] b) ſ…

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Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

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

A: ∫-22∫03∫04x2+y2+z2dxdydz

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Q: Question included in image

A: The given integral is,

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Q: Find the complete integral of 1 dz 1 dz 1 dz z dxz Ixe z z dx2 = x1 X2 X3.

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Q: Set up an iterated triple integral equal to √3-x² | = • S√³/3 SO √√3 x² + y² 3 2-₁/4-x²-y² 2y dz dy…

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Q: Q1 (a) Compute the multiple integrals of (i) V4-22 xy dxdydz (11) S, (8 – x² – y²)dA, where R =…

A: In this question we will use basic of calculus i.e concept of multiple integration. We will simply…

Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: Q4 Evaluate the double integrals: ||x+y+1)dxdy

A:

Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

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Q: (3) Evaluate the iterated integral , " (3 + x² +v²) dx dy.

A: First integrating with respect to x and then with y

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Q: ]] x² + y² 1+ y² dx dy

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Q: 6. How would you begin to numerically approximate the double integral: bd 1-SSS(x.y)dxdy ac

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Q: Sketch the domain of integration of the double integral (√(1-x²) La d.x dy x+y √(x² + y²) 0 0 and…

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 +…

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

A: