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

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A: Given integrals, 1.1 ∫(cos2x+sinx)dx 1.2. ∫x+1x2+2x+1dx 1.3. ∫eln(3x)+2x+1dx The objective is to…

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Q: 1. Compute the following integrals. (a) dx. (b) 2° sin(x³) dx.

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A: as per our guidelines, I am solving only the first question with both parts please resubmit other…

Q: 1. Compute the following integrals. 1 cos 3x dx b) VAr + 7 c) a) dx dx sin x / (In x)3 f) / d) ſ eª…

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Q: 1 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

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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: Evaluate the iterated integral: 2 sin(xy) dy dx п/2 1

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Q: 3 2 Evaluate the iterated integral x cos y dy dx. 2 3л 2

A: Ans= 5/2=2.5 For detail go through the solution...I have solved step by step in detail

Q: 5. Calculate the double integral f, 2x cos(xy) dA , R = [0,2] × [0, 7]

A: We need to compute the value of the double integral ∫02∫0π2xcos(xy)dydx. Since, this is simple…

Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

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Q: Evaluate the following integrals. [e² sec ³ (eª) da 1 2 6 tan¹ x dx I 3 4 √9-w² w² dw pln(4/3) et dt…

A: Given data:- ∫x2dxx2-152, x>1

Q: Evaluate The Double Integral sin(x^2+y^2).dA where R = ((x,y)|-1sqrt1-y^2≤x≤0,-1≤y≤1

A: We have to evaluate ∫∫Rsinx2+ y2dA ,  We transform to polar coordinates first then evaluate the…

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

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Q: 1. Evaluate the following integrals: SS (6yz - 2y' kixdy, s = [1,4] × [0,3] a. 1 b. ||| sin 2x dxdy,…

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Q: 4. Find the following integrals exactly. Show all working. (b) / 2='(1 + z")-1, dx

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Q: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

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A: first we integrate the integtal with respect to x therefore integrate with respect to y.

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

Q: Q. No.5 Compute the integrals: a) S* 4 sin* x cos?dx b) , cos 2y sin 5y dy

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Q: B)Evaluate the integrals: i) S ii) f/2/2 x 2² siny dz dy dx. rdrde,

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Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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

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Q: 2. Evaluate the following integrals. (b) § S, sin y² dy dx

A: Solution

Q: 1. Compute the following integrals. (a) dx. (b) x³ sin(æ³) dx.

A: We have to integrate both

Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: 3. ( ) The integral f S, sin(y²)dydr cannot be evaluated since f sin(y³)dy is not an elementary…

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Q: iii. Find the particular integral (P.I) of y" + 9y = cos 3x

A: To find the particular integral P.I of  y''+9y=cos 3x

Q: b) Evaluate the following integrals using tabular integration by parts 1) (3x² – x + 2)e* dx +x + 1)…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: ...... ... ... ...- Evaluate the iterated integral. 5. y cos(x) dy dx

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Q: -. Evaluate the double integrals a) F S, sin(x) dydx

A: Since you have asked a question with multiple parts in a single request we would be answering only…

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

A: Let's find.

Q: 2_ Calculate the generalized integral. x In r dx J. (1+12)3

A: The given integral: Calculate the above integral:

Q: Which of the following is not an improper integral? 1 dx cos x 2 cos x dx | cos x dx 0. 1 dx cos x 2…

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Q: /2 TT Sin (x ty) dy dx 0

A: Consider ∫0π2∫0π2sin(x+y)dydx = ∫0π2∫0π2sin(x)cos(y)+cos(x)sin(y)dy dx =…

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Q: 1. Evaluate the following integrals. 3r5 (a) / dr V2 – x3 2" + e2" sin(2") sin(2=) dx 2x +3 (c) / dx…

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Q: 15. Evaluate the integral ſo S, x²y² dy dx (a) directly, (b) integrating with respect to x first and…

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

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Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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Q: Find a particular integral for d^2y/dx^2+dy/dx= sin x

A: