Calculate the gaussian integral, e- dx, using the complex integration [residue theorem]

Q: In Exercises 29-76, evaluate the indefinite integral.

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Q: Evaluate the indefinite integrals in Exercises . .. by using the given substitutions to reduce the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (a) Consider the integral exp(t) dt. Use the substitution arcsin(t) = u to formulate this as an…

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Q: In Exercises 57-60, calculate the integral, assuming that f (x)dx = 1, f(x) dx = 4, f(x)dx = 7

A: It is given that, ∫01fxdx=1,  ∫02fxdx=4  and  ∫14fxdx=7

Q: Find the solution in the form of Fourier integrals: Ut- 3uxx = 0, u(0, t) = 0, |u(x, t) bounded as x…

A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: In Exercises 25-28, sketch the domain of integration and express as an iterated integral in the…

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Q: Find the solution in the form of Fourier integrals: U4-3uzz = 0, |u(x, t) bounded as x → ±0, sin r…

A: We are given the following second order partial differential equation : ut - 3uxx = 0  ;  -∞ < x…

Q: In Exercises 5-40, evaluate the integral using FTC I.

A: Given: ∫0π3cost dt

Q: Evaluate the integral. dt e dt = %3D

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Q: Evaluate the integral de. f(0) = Lo sinh 0 – a %3D “ OP- where a is a complex number (Im a + 0.)

A: Given function is  f(θ)=∫-∞∞θsinhθ-adθ or we can write it as f(x)=∫-∞∞xsinhx-adx     (1) since…

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

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Q: In Exercises 85-98, use the Change of Variables Formula to evaluate thedefinite integral.

A: Given:∫1017x-9-23 dxIntegrating formula:∫xn dx=xn+1n+1

Q: dx Consider ·S= using rationalizing substitution. x1/2 + x2/3 Find the integrand in terms of z.

A: Given

Q: Evaluate the integrals in Exercises 9– 18 It may be necessary to use a substitution first. x dx 9.…

A: We'll answer the first question since the exact wasn't specified. Please submit a new question…

Q: In Exercises 29-76, evaluate the indefinite integral.

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Q: In Exercises 49-54, evaluate the integral in terms of the constants.

A: We have to evaluate ∫-xxt3+1dt From Property of definite integral, we have ∫-aafxdx=2∫afxdx…

Q: What will you factor out from the integrand of ] csc°(3x)dx so that you can transform it to its…

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Q: In Exercises 15-34, calculate the integral.

A: We have to calculate integral ∫12212dxx16x2-1

Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: Find the solution in the form of Fourier integrals: U₁-3 = 0, uz (0, t) = 0, |u(x, t) bounded as…

A: We have the following partial differential equation : ut - 3uxx = 0  , x,t > 0 With boundary…

Q: Evaluate the improper integrals in Exercises

A: "Since you have posted two questions, we will solve first question for you. To get another question…

Q: In Exercises 45–48, calculate the integral, assuming that •5 .5 f(x) dx = 5, 8(x)dx 12

A: Given: ∫05fxdx=5, ∫05gxdx=12 To evaluate: ∫052fx-13gxdx Solution: We know that, ∫fx+gxdx=∫fxdx+∫gxdx…

Q: Eveluate the integrals in exercises (a-b) x 5-x cos (x+

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

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Q: u (x) = sin r+ u (t) dt

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Q: In Exercises 35-38, state whether TN or MN underestimates or overestimates the integral and find a…

A: Given the integral ∫0π4cosxdx

Q: nsi Sinhna (na)? 8. ) Sind( x) Sin y)

A: Given Fourier series, ux,y=∑n=1∞1sinhnπ8sinnπ2nπ2sinnπ2sinhnπy2+8nπ2-8cosnπnπ2sinnπx2sinhnπy2 To…

Q: What will you factor out from the integrand of csc°(3x)dx so that you can transform it to its…

A: the given integral,         ∫csc6(3x)dx

Q: Evaluate the iterated integral. cos(s*) dt ds

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Q: Use Romberg integration to compute R3,3 for the following integral cos x dx

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Q: In Exercises 15-34, calculate the integral.

A: Our Aim is to calculate the integral given below:-I=∫dxxx4-1 -(i)

Q: In Exercises 11-59, evaluate the integral using the appropriate methodor combination of methods…

A: ∫(3x2-1)x(x2-1)dx

Q: Use Cauchy's Residue Theorem, where appropriate, to evaluate the given integral along the indicated…

A: Given integral is ∮1(z-1)(z+6)2dz

Q: In Exercises 35-74, evaluate the integral using the methods covered in thetext so far.

A: ∫sec7θ tanθ dθ=∫sec6θ secθ tanθ dθ Now put, secθ=t⇒secθ tanθ=dtdθ⇒secθ tanθ dθ=dt

Q: In Exercises 85-98, use the Change of Variables Formula to evaluate thedefinite integral.

A: Given integral, ∫0π2cos3x sinx dx

Q: Evaluate the integral [I-÷+1]dx by the evaluation part of the Fundamental Theorem of Calculus

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