O Evaluate the following integral 2dr J a (3(ln z)2 + 12 In r 15)

Q: Evaluate the following integral using the Trapezoidal and Simpson’s rules with n = 10 In (x² +…

A: The integral is ∫02lnx2+1ecos xdx where n=10. By using Trapezoidal rule,…

Q: Evaluate the given integrals. z3+1 2. z+1

A: Explained below

Q: w'ew dw -1

A: Using integration by part's & definite integral.

Q: Q/ Evaluate the following integrals. (2²-2z+1) cosh z dz

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Q: 1 J z(9 – In² z}5/2* 피(9-

A: We have to evaluate the given integral.

Q: a) Evaluate the following integrals S(x2 - 2x + 1) dx. i- i- Jx cos x dx.

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

Q: 5. Compute the following integrals: (a) In x dx C y? +1

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Q.1) Evaluate the following integral dr (2e – 4e – 1)

A: To evaluate this integral by method of substitution

Q: Evaluate the following integral using the Trapezoidal and Simpson's rules with n = 10 In (x² + 1)e**…

A:

Q: 2ェ dr Vェ? +1

A: We have to find the given integral.

Q: Evaluate the following integrals (a) S Cos(2nWt)dt, where W is a constant. n/2 c3 (b) S,"7² S, r²…

A: Integral of cosx is sinx  Integral of sinx is -cosx.

Q: dx : Evaluate the following integral: 1.J. (32+x2)²"

A:

Q: 2. Evaluate the following integral using the Weddle's rule and h = 0.1. 1.6 1

A: The Weddle's rule is given as, ∫x0x6y dx =3h10y0+5y1+y2+6y3+y4+5y5+y6              .......1 Given,…

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

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Q: waluate the following integral 2dr J z (3(In z)2 + 12 ln z – 15)

A:

Q: 6. Let r>0. Evaluate the following improper integral:

A: the given integral is ∫-∞∞rr2+x2dx First solve the integral ∫rr2+x2dx r∫1r2+x2dx substitute x = ru…

Q: Evaluate the following integral using the Fundamental Theorem of Calculus. 3s2 - 6 ds .3 3 352 ds 3…

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Q: Evaluate the following definite integral using the Fundamental Theorem of Calculus. In 5 eXdx In 5 e…

A: To evaluate the integral using the Fundamental Theorem of calculus (1/7) integration (0 to ln5) exdx…

Q: I. Evaluate the following integrals. 1 1. -d.x J #(9 – In² a)5/2°

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Q: Evaluate the following integral. z+3 dz z(z? + 49)

A: Given integral is We will use the partial fraction decomposition to evaluate the integral.…

Q: Evaluate the following integrals: (3" – e") dx A 3* In(3) – e + C 3*+1 ez+1 +C x +1 x +1 3* - e" + C…

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Q: A. Evaluate the following integrals. S(e* + 1)² dx 3.

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Q: 2. The integral is given as follows: dr In(1+ ab) 1+ ar a. rdr By using the above integral. evaluate…

A: Given: that∫0b1(1+ax) dx =1a ln (1+ab)To…

Q: 1. Evaluate the following integrals using Cauchy's formula: (a) sin z -dz. Izl=1__z

A: (a). Given integral is ∫|z|=1sin zzdz As limz → 0sin zz = 1 So the given function have no pole…

Q: 1 dx 2. 0 (2x+1)Vx²+x

A:

Q: 7. Evaluate the following integrals : (») f (; 4 z) dz, (a) z-1 |z|=3

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

Q: Q.1) Evaluate the following integral et xp- J 2= – 4e* – 1) “r

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Q: Consider the following integral 3d.r (16-472)5 A suitable trigonometrie substitution to reduce it to…

A:

Q: Evaluate the definite integral. •4 ti + t?j| dt 3 |(7 - 1) 2 17 3 173 3

A: The value of the given integral is 1/3(173/2 - 1)

Q: Q1/ Solve the following iterated integral: SL. ex-ydA, R: 0sxs In 2, 0sys In 2.

A: 1) We have to solve the iterated integral ∫∫nR ex-ydA where R= 0≤x≤ln2 ,0≤y≤ln2

Q: Evaluate the following integral 2dr (3(ln r)2 + 12 In z – 15) 15)

A:

Q: 5. Evaluate the following integrals Đ с Z e CASTTZ ***** ・dz, c: |Z-il=1.5 ans: -ui sinh 1/2 *****

A: Evaluate: ∮Cezcosπzdz where C: |z-i|=1.5

Q: 1 e 9- z

A:

Q: Sn/2 "/2 cot3 x dx

A: Given: ∫π4π2cot3xdx

Q: Evaluate the following integrals (taken anticlockwise) using Cauchy's theorem: (f) P.„(²+1)² eiz dz…

A:

Q: The evaluate the integral (1) is equal 13erf(t) dt

A: The function, erf(x) is defined as erf(x)=2π∫0xe-t2dt .

Q: I. Evaluate the following integrals. 1 d.x J #(9 – In² x)5/2* 1. -

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Q: Evaluate the integral given below. Vīn3 e dædy (2VIn3 4/5 O 3vln3 In3 1

A: The given integration is  

Q: 1. Evaluate the following integral over 0 <a< In 2 and 0 < y < In 2:

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Q: Compute the following integrals: (a) ==3 z(z – 2)3

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Q: Q.1) Evaluate the following integral 2dx J r (3(In r)2 + 12 In r- 15) |

A: We have to find indefinite integral

Q: Q1/ Solve the following iterated integral: SL. ex-ydA, R: 0<x< In 2, 0 <y< In 2.

A: Given integral I=∫∫R ex-ydA     ;  0≤x≤ln2   , 0≤y≤ln2

Q: A Evaluate the following integrals. 1. fx² In x dx 2. S tan-ix dx

A: Let I=∫ x2lnxdxApply integration by part,I=ln(x)∫x2dx-∫ddx(ln(x)∫x2dxdxApply power rule…

Q: Evaluate the following integral from a=-0.4 to b=7.6 with single application of Simpson's 1/3 rule b…

A: The solution is given as

Q: a) Evaluate the following integrals i. S (In (x) dx+J(ax²+ 5x)]

A:

Q: 7. Evaluate the following integrals : (») f (- 4 - z) dz, (a) z – 1 |z|=3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the following integral using Simpson's 1/3 rule, with n = 8 5 2.5 sin(1.5 x) + 1.22…

A: Given function is  f(x) = 2.5sin(1.5x) + 1.22cos(0.75x) + 1.75ex h = b - aN = 5 - 28 = 0.38

Q: A. Evaluate the following integrals: 1. Sx² e*³dx et3

A: To evaluate the given integral.

Q: 2. Find the following integral: NT u sin du. n.

A: