Question 13 Evaluate the integral: f (z² + y²) ½ dydz -1/2 O v2 + In(v2 + 1) O In(v2- 1) O v2 - In(v2+1) O In|sec e + tan 6| + C

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

Q: Question 19 Evaluate the improper integral: e-2 x dx a) 1 b) O c) d) -2 1 e)

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Q: Question 7 7 da a4 1 Calculate the integral: a) OIn|2 - 1| + C b) O미-1 + C 7 c) 0arctan(2) + In|(x -…

A: See the attachment

Q: Find Particular integral (P.I) (D² -1)y =18

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Q: Еxercise: 1- Use the Composite Trapezoidal rule with the indicated values of n to approximate the…

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Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

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Q: The particular integral of (D – 1)y= x i,

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Q: 4 x Calculate the integral: dx 72 6, 2 x a) O 3 +C 18 arcsin b) O-2 aV9 – x² + 18 arcsin )+c 2 x c)…

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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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Q: Find the Fourier integral of the function f (y) = e¬"y when y > 0 and f(-y) = f(y) for n > 0 and…

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Q: Find the complete integral and singular integral of z = px + qy+√√1+p²+q²

A: Given partial differential equation is z=px+qy+1+p2+q2. We have to find the complete integral and…

Q: 3. Use a triple integral to derive the formula f *+ + = 1. = 1.

A: Given: To derive the formula for the volume of the ellipsoid by using a triple integral. x2a2…

Q: 3 2(x²+1)7 Write down an integral that gives the ARCLENGTH of y on the interval from x = 0 to x = 2…

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Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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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: The value of the improper integral 42 x² e¯¤* dx 1 - 14e 14e-1 - O 14e-1 O 42e-1 O – 42e-1

A: Explanation of the solution is given below...

Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

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Q: Find the Fourier integral of f(x) = e-k* when x>0 and f(-x) = f(x), hence prove that cos(wx) dw w…

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Q: Question 8 Evaluate the given double integral by changing it to an iterated integral. JJ xy dA; S is…

A: Note: Graph the triangular region and find the limits

Q: dx (1 – e²)² -1

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Q: 3. Evaluate the iterates integral: SL(x-y) dy dx

A: We have to solve

Q: 1. Prove that L{cos(at)} cos(at)dt integrating by parts twice and the evaluation of the improper…

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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: Question 1 Calculate the integral: /3x In (x°) dx a) O In(x*) + C 3 b) O* In(x*) – r + C In(x*) + *…

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Q: 1. Evaluate the iterated integral. .Só Sa(x² + y) dyd.x b. S So sin(x²) dydx 2y -1 x+1 dydx с.

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Q: 14. Find the equivalent integral of * S x(x+1) O-f3dx + f 3d x+1 dx OS÷-1# R x+1 01 Of //dx -…

A: Here we have to apply partial fraction.

Q: In this question, you are asked to investigate the following improper integral: (х-3) -13 dx 10.1…

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Q: The Fourier cosine integral of J (x) D 0, 2, 0<x<3 is 0<x О а. 4sin(@)cos(@x) do O b. 8 sin(3@)…

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Q: 3. The integral of an t dx is b In|sec(In(2x)ª)|. What is b? A. 1/2 В. 1/4 с. 2 D. 4

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Q: The particular integral of (D² +1)y = x is

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Q: 1. Evaluate the integral using FTC Part 1. | (23 – 2a) dæ 2. Evaluate the integral using FTC Part 2.…

A: As per guideline we have to solve only one question

Q: 7. Find the Lebesgue integral over [0, 2] for the following function. f(x) = { , EQ 3z +2, IEI %3D

A: Given  f(x)=x2        x∈Q3x+2  x∈I

Q: QUESTION 6. Use an appropriate change of variable to evaluate the double integral: - x d A, cos y+ x…

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Q: Question 6 Estimate the integral 1 dx by Simpson's rule using n = 8. Vx3 + 4 a) 00.9361 b) O1.0212…

A: given integral :

Q: Question 1 Calculate the integral: (xº) dr a) 지 15 ² +C b) * In(x°) + C 15 e) Or In(x*) – +C d) O-*…

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Q: Question 3.2: Let G : z(1) =-1+÷e“, 0si< 2n and C, : z(1) =1+÷e“, 0si<2n and C: z(1) = 2e“, 0<IS27.…

A: Let the given domain isC1:zt=-1+12eit,for all 0≤t≤2πC1:zt=1+12eit,for all 0≤t≤2π andC:zt=2eit,for…

Q: S For x1/2 x−x³ dx and using the substitution u=x1/2, the resulting integral takes the form:

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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: Question 20 In evaluating |x V4-x dx by substitution, if u =4-x then what will be the resulting…

A: We have to find out the integral

Q: dx The integral can be rewritten as VT - x 00 lim (-2+ v1– 3) S--00 lim (-1+2v1– s) s--00 B lim (-2+…

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Q: Question 5 Evaluate the double integral over the given region. 8x sin xy dA, R:0 sx <T, 0 <y s1 7C…

A: Given that, The integral is following, ∫∫R8xsinxy dA R : 0≤x≤π, 0≤y≤1 We have to find the value of…

Q: c) Evaluate the integral e* (x + 1) - dx, VI – x² using 3-points Gaussian quadrature.

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Q: [1 0SxS1 Given fx) - {-1 -2sx 1 what is the value of the Fourier integral of at r-1 O A.-1 O B. 1…

A: Fourier series and function value

Q: Question 2.6. Use the Riemann integral to prove that for f : [a, b] → R Riemann integrable and f 2…

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Q: Solve the integral equation* 1-a, 0 sas 1 0 ,a>1 . f(0) cos ae de = %3D Hence evaluate sin t dt.

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Q: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

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

Q: 1-X let dx , write the integral by using Beta function 0. 1 3 .a 2'4 1 B 2'2 .b O 3 .cO 2 2 1 B 4 2…

A: It is on the direct formula Beta function

Q: Question 5. For this question consider the standard result: 1 ;du = tan¬1 u + u? (1) Only using (1)…

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