a²f, a2f ax ay2 ду? f(x, y) = In(x2 + y?) + tan-1() A- Show that = 0, where B- Evaluate the integral 1-x2 Li dz dy dx 3-x-y 1-x2

Q: tan -1x dx Evaluate the improper integral /. 1+ x2 1

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. x dz dy dx -6+x²+y?

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Q: What is the total differential dW given W- In(x+y +z')?

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: Q3\ Evaluate only TWO integrals A-ſ tan5 (x)sec*(x)dx P ( sin(x)+esin (x)+sex³ (x) B-S sec (x)…

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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: b2 a? 2 Use Jx dx a<b, to evaluate the integral x dx. 2 2 a x dx = 2 (Type an exact answer in…

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Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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Q: dx Given that /2 || 1+sin² x 2/2' ) please evaluate the double integral CT/2 pT/2 1 dx dy (1+ sin?…

A: We have to find value of given Integral.

Q: x-2 3. Evaluate the integral S (t3 In t i + 3t³ sin (t*) j+ x(x+1) k) dt.

A: Integration: - Integration is the process of finding the anti-derivative function of the given…

Q: 1. TⓇ S (a) Find the general indefinite integral. 2t² + t²√t-1 t² dt

A: topic- definite integral

Q: Exact difterential egation 4. (1+In(xy))dx+ 1+ dy=0 y,

A: Given differential equation is, 1+lnxydx+1+xydy=0   ...................(1) Comparing with Mdx+Ndy=0…

Q: Evaluate the integral. cos y dy 2, siny+ 3 sin y - 28 S: cos y dy 2. siny +3 sin y - 28 (Type an…

A: To evaluate∫cosysin2y+3siny-28dy

Q: (2– sec?x) cma/e°sec³x sec( 3A – x) What should be the value of A for dr to be integrable using the…

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Q: Vr+1 -dx the integral || u? 3.

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Q: Test for exactness (2ysinxcosx - y + 2y?ey )dx = (x - sin?x - 4xye*y )dy %3D solve exact de,…

A: First we have to check exactness then we solve the differential equation.

Q: - sec?x)emG/e sec³x dr e In (a le) What should be the value of A for to be integrable using the…

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Q: 0; x 0

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Q: In(y²) dy 3y

A: Given- To do- Evaluate the integral by substitution method.

Q: 1 I = dx V(a-a)(x-a-2b)

A: Given data: The given integral is I=∫1a-xx-a-2bdx. The given integral can be written as,…

Q: 6.3.28. Evaluate the integral. using U substitution integrate (x^2)sqrt(x^2-1)dx

A: Use substitution method, to evaluate the integral

Q: Q2) Evaluate the integrals 1) f (sec 0 tan 0) VI + sec 0 d0 , 2) sa+v2 du

A: 1. ∫secθtanθ1+secθdθ Take  1+secθ=tsecθtanθdθ=dt Therefore,…

Q: aw Find for w e" sin p where ax p = sin x q = z2 In y x- at (x,y,z)3글) %3D z2 e sin-1 x = Hint: dx…

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Q: S(2- sec?r) elnale sec'x sec( 3A – x) What should be the value of A for - dx to be integrable using…

A: The given question has been solved in detail and option C is the correct answer.

Q: 1- 2- 3- 3-Evaluate the integrals in Exercises: [ sect? (x - 1) dx sech² s sech Vt tanh Vt dt Vt…

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Q: 2- 3- Evaluate the integrals in Exercises [² dx L₁3 3 dx 3x - 2 dy 1- 2. S sec y tan y 2 + secy

A: We can answer all the three questions as below.

Q: Q5 Use Green's theorem to evaluate the line integral (cos.x+2y)dx+(x – sin y)dy C where C is the…

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Q: -5e 1 Evaluate the integral: dx. 1 x A. - - 1 5e B. 1+ In 5 C. 0 D.00

A: We have to evaluate to integrate

Q: a) Find the indefinite integral of the function 1 y = 3t2 + 2e3t +- + 2 cos 3t | b) Calculate the…

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Q: Q.3) (a) Evalute (x² – y²)dx + 2xydy, along the circular arc C that is upper half circle oriented…

A: Given - ∫Cx2 - y2dx + 2xydy To find - Evaluate the given integral along the circular arc C that is…

Q: Evalua the iterated integral. 8. (x + y) dx dy -1J1

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Q: Q2 Show that the region included between the cardioids r=a (1+ cos 0) r = a (1- cos 0) is given by:…

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Q: (a) Check if u(x)= cos2x is a solution of the integral equation u(x) = cosx + 3 f k(x, t)u(t)dt,…

A: It is given to solve only Part(a) Given that u(x)=cos 2x The given Integral Equation  is: u(x)=cos…

Q: sec 2x In evaluating the integral dx, using the appropriate formula, the du = M. V1+tan 2x •1/2…

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Q: -. Express lin (we (2 4 ) - 2 (2 + 2)) 2 2+ as a definite integral, f sec n→∞ N i=1

A: Given  limn→∞3n∑i=1nsec2+3in-22+3in

Q: (2x +)x dx | (28 + 4x5 + 4x²)? sing u-substitution and transformation of the integrand, then the p…

A: We will solve the integration using substitution.

Q: dy dx Assume x and y are functions of t. Evaluate for 4xy - 7x+4y3 = - 92, with the conditions dt =…

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Q: (2- sec?x)eln (afe°sec³x sec(3A – x) What should be the value of A for dx to be integrable using the…

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Q: Q.1 Find the double integral le cos x² dA Where R between : x=-y/2, x=1 and y=-2 , y=0. Q.2 Sfr…

A: Please see the explanation below

Q: 1 point) Let f(x)dx = 3 and "(f(x))*dx = 13. Find the following integrals: S. cf(z)dz = v)*dx – (J,…

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

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Q: 1-(x-1)? x+ y 2 x + y Evaluate the integral: dy dx

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Q: 5 x Evaluate the improper integral: dx lo V4- x2 a) O20 b) O10 c) 05 d) Odiverges e)O15

A: Given the integral ∫025x4-x2dx.we need to evaluate the given interval.

Q: (2– sec?x) eln (xle) sec(3A – x) 'sec³x What should be the value of A for to be integrable using the…

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Q: a) [ „J: Evaluate the integral (4x + 1) In x dx b) ' . Evaluate the integral fou 6 tan' x sec* x dx…

A: a) Given:       ∫4x+1ln x dx Integrate by parts: ∫fg'=fg-∫f'g where f=ln x , g'=4x+1           f'=1x…

Q: sin-cos-sino d®? 2 2 What is the integrable form of 2- 1 du B 2 | cosu du 1-u² du O -2/- D sinu du A

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Q: xP-1 7. Find the relation between p and q that makes integralS dx con- 1+ x9 vergent. A) p=q B) q>P…

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Q: dz (x2²–x³) 1/3dx Using the substitution *=-, dx= - the integral reduces to x3 (22– 1) 1/3 -dz A) -…

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Q: S(2- sec?x) eln ale)sec³x sec( 3A – x) What should be the value of A for dr to be integrable using…

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