Evaluate the improper intergal 1 -dxusing the residue theorem. (x² + 25)? 8.

Q: Evaluate the integral. / 16 – t² dt 16 -1² dt =

A: Put t = 4sin(theta) so that you can get a perfect square term inside root ....and then we can get a…

Q: nt) Using the u-substitution u = 7x2 + 4, identify ƒ such that the integral dx takes the form | f(u)…

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Q: Use Residue theorem to evaluate dx - x2- 8x+ 17 00

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Q: Compute the Cauchy principal value of the following integral using residue theory details): 2+1 dz…

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Q: G.. Evaluate the fallowing real integrals by residue. theerem 3 -bm e 응) co3 mx (x4a?) Cx+b?)

A: This is complex analysis problem, we apply the residue theorem to solve the problem.

Q: 3 Evaluate the integral de using the two-point Gaussian quadrature rule O -|4 1035 N/N N/W 끔

A: We have to evaluate the integral ∫−3311+x4dx by using two-point Gaussian quadrature rule. Here,…

Q: Evaluate the integral fa*(2* – 2)" dz 15 by making the substitution u x4 – 2. -

A: Given : ∫x3(x4-2)15dx

Q: Evaluate the integral f 2x (x² + 6)° dx using the substitution u = x2 + 6. | 20(x² + 6)* dzx +C

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

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: 2 c2 Reverse order and evaluate the integral S, 2y2 sin(xy) dydx

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Q: Value of the following integral by mean of the Cauchy Residue Theorem is 1 ni = zp- z2 sinz 3 JEl-4…

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Q: dx 2 -o x+4x+5

A: The general form of a complex number is given by , where a, b are two real numbers and . Any complex…

Q: Evaluate the improper intergal 1 dxusing the residue theorem. (x2 + 9)?

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Q: Graph the integrand and use geometry to evaluate the integral. 6 2) s V36 - x2 dx -6

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Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: Evaluate the improper intergal 1 dr using the residue theorem. (x² + 4)?

A: Solving imroper integral using residue theorem

Q: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +C

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Q: 2. Use Cauchy's Integral formula, Evaluate the foll D I - & tantz Z² C: 171=1

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Q: Evaluate the integral f 2x (x2 + 7)° dx using the substitution u = x2 + 7. 2.x (x² + 7)° dx +C

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Q: dx%3D 9+x²

A: Solution is given below:

Q: (2- secx) secx sec(3A – x) eIn (xle) What should be the value of A for to be integrable using the…

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

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Q: Using the Cauchy residue theorem evaluate the following improper integral cos 2 dx (22 +1)2"

A: ∫0∞cosxx2+12dx=∫0∞cosxx+i2x-i2dx Let fx=cosxx+i2x-i2. Then f has singularities at x=±i with…

Q: x +1 -dx x3 +1

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Q: tan (in |4x2|) dx is bin sec (In |(2x)ªl)| + C. what is ba The integral of A B) 4 © 1 1

A: Topic:- integration

Q: Use the Residue theorem to evaluate the integral fe(z-2)dz.

A: Use the expansion of e1z  =1 + 1z + 12! z2 + 13! z3 + ...  Hence ∫e1z(z-2)dz = ∫(z-2)1 + 1z + 12! z2…

Q: 215 5. (a) Transform the real integral Pz dr into a complex inte- gral clearly specifying the…

A: We transform given integral into complex integral.

Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

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

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0&lt;z&lt;π…

Q: Use the Midpoint Rule with n = 3 to approximate the integral 10 %3D (7x - a2)da

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Q: tan (In |4x²|) dx is bin sec (In |(2x)^)| + C. what is b? The integral of (A 4 1 B c) 2 1 D 2

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Q: The improper integral 2dx is 1-x2 0.

A: π

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

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Q: Evaluate the triple integral: 3 ₂2 0 (x+y+z)dydxdz

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Q: - use the Cauchy Residue Theorem to integrate the given function around the

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Q: Apply Cauchy integral formulå to find the value of the integral: sinz Se dz; where C:|z| =. Also…

A: Note:- As per our guidelines, we can answer the first one as exactly one is not mentioned. Also, for…

Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: Use Cauchy's Residue Theorem to compute the improper integral (x + 3) sin(x) dx (x2 + 1)(x² + 4)2 00…

A: Given that ∫-∞∞x+3 sinxx2+1x2+42dx Using Cauchy residue theorem, we can written it as ∫-∞∞z+3…

Q: xcosr (i) Find the Cauchy principal value of the integral dr. ² + 4x + 8

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Use the Residue Theorem to evaluate the a? integral dx + x2 where a>0

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Q: Evaluate the integral. ƒ ƒ6(x³ - y³)²dA = □ (Type an exact answer.) R

A: ∫-11∫016x3-y32dA

Q: Evaluate the integral 53.3904 | (1-e0183551) dx by using third-order (two-point) Gauss quadrature.…

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

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Q: Consider the definite integral. (18x – 1) e9x²-x dx Let u = 9x? - x. Use the substitution method to…

A: We have to find the integrand after substitution.

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,…