2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

Q: H.W: Evaluate the integral (x²y - 2xy) dydx 1. 30 0-2

A: As per your query the solution of the question no 1 is given in the next step.

Q: 2. Calculate the following integral: dx (a) sinh? x – 4 sinh x cosh x + 9 cosh² x +*) u (1– x²)² x…

A: 2) a)

Q: Express lim E=1 Ax ||PI0 as a definite integral where P is a partition of [0,2]. k%3D1

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Q: Determine the following indefinite integral. ( 2 + 3 cos(y) 2 dy sin²(y)

A:

Q: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

A:

Q: Evaluate the indefinite integral. 2 (t) – 7e' + 8 + 1 + 12 2 sin(t) – 8 cos(t) + sec- dt = +C.

A:

Q: Evaluate the indefinite integral. asin (a)cos(2)dz: + C %3D

A:

Q: This problem extends Example 5.14 and Exercise 5.19, allowing us to compute the following integrals…

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Q: T 3. fz sin4 y cos7 y dy 2

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Q: Evaluate the following integral.

A: The given integral is,

Q: Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

A:

Q: 2. Use the Definition of Residue to show that: dz -ni Izl=1 z² sinh z 3 Where 0 < |z| < T.

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Q: Evaluate the following definite integral. 8y dy y-4y-12 8y dy =D y-4y-12 (Type an exact answer.)

A: Dear student our policy is to answer first one in case of multiple question, so please repost the…

Q: Evaluate the iterated integral. T/4 1 Tv cos(x) dy đx

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

A: Use change of order of integration.

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

A:

Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: 2 Evaluate the definite integral 16sin(t)cos (t) dt.

A:

Q: Evaluate the following integral. T/2 1 1/4 . sin TX cos 2y sin 2z dy dx dz 0 0 0 T/2 1 1/4 sin TX…

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Q: Find the indefinite integral cos t dt. 4 cos t dt=

A: We have to find solve

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: 4. Use residue theory to calculate the following integrals: 3x (a) P.V. · Loo (2²+49) (2² - 2x + 5)²…

A:

Q: 2m 28. t sin 2t dt

A:

Q: Choose the most appropriate answer: Evaluate the integral : J(e- 182 + sin 11x) dx -18x e + cosll +C…

A: We need to evaluate the following integral : ∫e-18x + sin11xdx

Q: Prove that for all r € [1, 00), – sinh (- |cosh-(x)|) = vVI² – 1.

A: We know that: Cosh-1x=logex+x2-1  and  Sinhx=ex-e-x2. And, Sinh-x=-Sinhx. Therefore,…

Q: The modified Bessel function I,(x) has the integral representation 2 7/2 El cosh(x sin 0 )do. n Jo…

A: Given:

Q: I don't understant this hw problem

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Q: Evaluate the following real integrals by residue theorem 3 03 S <-1 X Sin mx X4 +1 OSH dx πT -m/√z…

A: As per the question we are given an improper integral from -∞ to +∞ and we have to evaluate it by…

Q: Evaluate the integral (10 + sin t)* cos t dt 14 using the substitution u = 10 + sin t. 14 10 + sin…

A:

Q: (Find the integral curve of the following equation passing through the given point). y = 4 cos(x),…

A: Given dy/dx and point we have to find equation from this

Q: The modified Bessel function 1,(x) has the integral representation 2 16(x) cosh(x sin 0)d0. N Jo Use…

A:

Q: Evaluate the integral sin^4 e de from 0 to Tt/2 * T/4 O 2r/3 O 31/16 О З1/5

A: We have to evaluate the integral ∫0π2sin4θdθ. Use the reduction integral formula, which is given…

Q: Find cosh r In(sinh a)dr.

A:

Q: Evaluate the integrals "m/4 tan → 53. yeon sin t dt sec² t dt 54. x^(1 + Inx) dx alnx - dx 55. 56.

A:

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

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

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

A:

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

A:

Q: separate the following into real and imaginary parts tanh(x+iy) sinh(x + iy) coth(x + iy)…

A: Given; i) tanh(x+iy) ii) sinh(x + iy) iii) coth(x + iy) iv) cosh(x+iy)

Q: Using Cauchy's residue theorem, evaluate the following integral along the given curve: zel dz ; C :…

A:

Q: The modified Bessel function I,6x) has the integral representation /2 2 1(x) = cosh(x sin 0 )d0. Use…

A: We will use given value of x and mentioned process ( trapizoidal / simpson ) to find value of…

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

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

A:

Q: Evaluate the integral cos (x) sin(x) dx 13 using the substitution u = cos(x). cos(x) sin(x) d.x ,13…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the integral: ( ) sect tan ti +tcos 2t j+sin² 2t cos 2tk 1k)dt

A: the given integral is: ∫0π4sect tant i^ +t cos2t j^ +sin22t cos2t k^ dt we have to evaluate the…

Q: 2. Find the following indefinite integrals. (a) / sin(In(x)) xp (b) / º etan-(x) dx x2 + 1 sin(t)…

A: (a) ∫sinlnxxdx Let; lnx=t⇒1xdx=dt     =∫sint dt=cost+C put again: t=lnx =coslnx+C Result:…

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: Evaluate the definite integral. integral (lower 0, upper 3) t^3 sin(t^4) dt  =

A: We have to solve the definite integral

Q: Determine the following convolutions by integration (a) 1 * sin wt (b) et * e

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.