How Find 7.J {(H) = 2(-1)** uck-1) Ans: 2Z ē

Q: ,2 2. 6+t dt

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Q: 14. Evaluate the integral: | ze dz. 1

A: Integrating by parts.

Q: Evaluate the integral of ax^2 e^-bx dx

A: We will use the "integration by parts" method to find the evaluation of the integral.

Q: Use the fundamental theorem of calculus part 2 to evaluate the 16 integral: S 3/rd 9 Note: Convert…

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Q: 1 Prove that 3 dx s VI VI

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Q: 5. Find the indefinite integral 6.x²dx (2x³ + 7)3/2

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

Q: To evaluate the integral 1. 7 64 + x² -dx,

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Q: Calculate the exact value of each definite integral in Exer- cises 47-52 by using properties of…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: -25 Evaluate the integral: dax x²Vx2 +25

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Q: 9. Evaluate the integral J 4x2+9 1 dx

A: We can solve the integral as below.

Q: 4.3 Use the calculus of residues to evaluate the following integral (x2- dr. + 1)2

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Q: Evaluate the integral: */64 – a°dz .3 2 -

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Q: (-1- i iNT (-1– i VN)e™N¤ 3

A: See the attachment

Q: 2) Evaluate the integral S inx dr 2.

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Q: 10. It has been lo ponents produced in a certain factory are de hundred is drawn from each day's…

A: A random sample of size one hundred is drawn; n=100 1% of electronic components are defective;…

Q: 7 Evaluate the improper integral, if exists : dz (5 - 2)3

A:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: Evaluate the indefinite integral. 2 -dt (t + 8)°

A: Given integral :

Q: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: 6 Strange fact: 8(2x) is different from 5(x). Integrate them oth from 1 to 1.

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Q: 12. Suppose that g is integrable and that g(x)dx = -7 and [8(x)dx = 2. d: g(x)dx

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Q: Find a general solution of each reducible second-order differ- ential equation y" = 2yy'

A: Recall the chain rule of calculus:

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: Evaluate the definite integral. '1 3 + 7t³j+ Vik) dt /-1

A: Consider the given definite integral

Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: 2. Use Cauchy's Integral formula, Evaluate the following • I= sin4z ,IZl= 3

A: I am attaching image so that you understand each and every step.

Q: Evaluate the Integral / tanh (2x)đx. A @ --n|cosh(2x)| + C B -In|cosh(2x)| + C © 21n|cosh(2x)|+ C D…

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Q: Explain Bessel equation and Prove that 2 (n + 4)Jn+4x (i) (ii) In+3X + Jn+5X = 4J"n = Jn-2 – 2Jn +…

A: The objective is to explain Bessel equation and prove that  (i) Jn+3x+Jn+5x=2xn+4Jn+4x (ii)…

Q: Evaluate the indefinite integral. 7 dt 7 (t + 4)"

A: Given,            ∫7t+47dt

Q: 16j Use integral tables to evaluate, 3

A: I=32∫ 1x9x2-1 dxu=9x2-1du=18x29x2-1dxdx9x2-1=du9xHence;I=32∫ 1xdu9xx2=u2+19I=16 ∫ 9 duu2+1

Q: ar integral of the c 3 – 7D2 + 7D – 2

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Q: 2. Use the Intermediate Value Theorem to show that 2.x 3 - if – 3 0 has a zero on the interval [-2,…

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Q: 1 Compute the integral J -з (х+2)3

A: Given integral is ∫-33dxx+23 . Obtain the singularity. x+2=0x=-2 The function undefined at x= -2.

Q: Evaluate the indefinite integral. dt 6. (t+ 10)°

A: Use the substitution method and simplify the expression than integrate.

Q: 5. Evaluate the integral " Vtan o dex 1. de in terms of beta and Vtan gamma functions.

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Q: Evaluate the following integral. ∫ 2z5e1-z dz

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Q: Evaluate the indefinite integral. (7z + 7 71 + -dr Jz² +1

A: Given,          ∫7x+7x2+1dx

Q: 23+dt (4+3 Co+ 3+)5

A:

Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

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Q: 7. | (x² + + 2x) cos x dx

A: Apply the integration by parts in the given integral. Let  u=(x2+2x) ; dv=cosxdxThen,du=2x+2dx ;…

Q: 4 Calculate the integral: dr 9 x2 + 18 z + 18 4.

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Q: 18. Show that Ein d(k)³ = (Ekin d(k))² for all positive intege m

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Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

A:

Q: Choose the most appropriate answer: Evaluate the integral : S(19 Inx) dt O 38(2 ln 2 + 1) o 19(2 ln…

A: The integral is ∫12(19 ln x)dx

Q: (integral of -4 to 4) of 5*cos(3t)(delta(t))dt

A: Here,

Q: Prove this equa tion analy tic fcz)z Ln /21+iargz Ln 12|+iarg

A: Equation proving in analytical way

Q: 3 In z/4 tan (2)+cos(r) gives a positive number. 3 3. The integral f dæ, when evaluated, O True…

A: Check if the given statement is true or false.

Q: 3-Expand In [x? sin³ x /vx2 +1]

A: