2. Use Cauchy's Integral formula, Evalnate the following. • I= 6 Sin4Z :(Z-4)3 IZ1= 3 I = . tanttz C: Iz-il= ,12-il=2. %3D Z(Z-21)²

Q: a) Solve the following iterated integrals holding Fubini's Theorem. 1. 1 '(x+y)dydx

A:

Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

A:

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

Q: In Evaluate the integral: ₁²t² fln s t teu du ds dt

A:

Q: Calculate the iterated integral A 67 5x cos y dydx. 1 2n 5

A: Explanation of the answer is as follows

Q: - Evaluate the iterated integral 3xyz dz dy dz.

A: Definition. • In calculus, an iterated integral is the result of applying. integrals to a function…

Q: 1- 22 19ze dx dz dy 5

A:

Q: х cos 4x dx; и 3D х, dv cos 4x dx =

A: Given that  u = x ;  dv = cos 4x dx and we have to integrate by parts the given integral that is ∫x…

Q: 1 6. Evaluate the given integral using suitable substituion COs(V도+ 3) dr

A:

Q: Find the definite integral using the Fundamental Theorem. 2 1 dt 4t NOTE: Enter the exact answer. ~2…

A: Definite integration problem

Q: Evaluate the following integrals (2х — 5) 4. dx 2 4x - 4x + 26) | TC 2 1 5. do esc°(20) sec²(2 csc…

A: As you have posted multiple questions so I will answer only first question as per guidelines.

Q: Evaluate |- e*dz where c is |z|=3 using Cauchy's integral formula „(1+2),

A:

Q: 3.2. Prove directly from the definition of Itô integrals that t t | B?dB, = B - | B,ds .

A: The answer is given below

Q: calculate the result of the following integrals Sinł dz 19423,2 A) IZI 22 Z +4 dz IZI :4…

A:

Q: 1) Evaluate the following iterated integral. 2/2 sin(2y) SS dydx y 0x

A: Use change of order of integration.

Q: 1. Evaluate the following integral, using the Cauchy integral formula: COs z dz 22 --2 |=-il=2

A:

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…

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: Use the method of u-substitution to evaluate the given integrals. 4t dt 2 – 812

A:

Q: The evaluation of the integral - de is +In 3 (C) 0 cos3e (i) 4 (ii) + In 3 3. (iii) None of these…

A:

Q: Evaluate the integrals

A: Solution -  Given Integral equation - y = ∫π201+cos2t2dty =12∫π20dt + 12∫π20cos2t dtUsing…

Q: +0o 34 Evaluate the imporper integral f10 , dæ divergent 17 In 9

A:

Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: 2. Compute the following integrals: sin(it) dt; t - T 1 -dz; 1 22 (1,1) -

A:

Q: The given integral is equal to cos 3t dt 5 + 3 sin 3t O (1/3) In 15 + 3 sin 3t| + C O (1/9) In 15 +…

A: To find out the integration.

Q: What is the integral of f cos (2t)dt? O sin(8t) + sin(4£) +24¢ + C 64 O None of the choices O cos"…

A: Indefinite Integration

Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

A:

Q: 1- Find the integral of: 2 cot - de 3 7/2 A- B- dr Vr

A: (A) Given integration is : ∫π2π2cotθ3dθ Use property of integration ∫cotaxdx=logsinaxa+c

Q: Evaluate the integrals. /3 (5 sec t tan t)i + (4 tan t)j + (3 sin t cos t) k dt =…

A: The integral is, ∫-π 6π  35secttanti→+4tantj→+3sintcostk→dt The first coordinate is∫-π  6π…

Q: Evaluate the integrals. In 3 6tei + Te'j+ 2 ln tk dt 18(In(3)-1)i+7(3-e)j+2(In(3))(

A: Topic- integration

Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

A:

Q: Find the integral. 5. S(2ri+j+k)dt 6. sec' ti+- -jdt 1+r

A:

Q: Evaluate the integrals of five only of the following: 1) I = St2 e" dt 2) I = Se-2x sin 2x dx 3) I =…

A: Please refer the attached image for complete solution.

Q: Evaluate the integral using the given substitution. SV cos (2-7) dx Select one: 3/2 sin (x - 7) + C…

A: topic - indefinite integral

Q: Can i get help step by step with this problem?

A: Given:

Q: The solution of integral Vu2 + u +1 du is:

A:

Q: /4 6. u(x) = sin (2r) - zu(t)dt-

A: To solve the integral equation using direct computation method.

Q: Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let…

A:

Q: 5. Evaluate the following integrals3 sin ttZ dz C: İz-il 471 =D2 ans: C. 3. coshz -27 ans : Icz²3iz

A: By residue theorem, we can solve these problems.

Q: Evaluate the iterated double integral 2 b.) √ √ ² sinπTy ³ dydx

A:

Q: In Evaluate the integral: Sto st² sin s teu du ds dt

A: The given integral is: I=∫12∫tt2∫0lnsteududsdt   The Power Rule: ∫ax+bndx=ax+bn+1an+1+C

Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: 5. Evaluate the following integrals 3 sin #Z dz, c 1z-il=2 24 -4 ans: 3 co shz

A:

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

A:

Q: In (x le) (2– sec²x)elmtafcsec?x sec(3A – x) - dx to be integrable using the formula 'du? What…

A:

Q: Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises 1-24. 2. а. rV x3…

A: