COSz Show, without evaluating the integral, that z2(z + 1) *26 5 zp-

Q: 3/2 1/2 q q 1 2 dq

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Q: What is the integral of f(x) = X within the interval [3, 6]? %3D 5. 4+ 3- 2- 1 O Area = 18 O Area =…

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Q: r In(z² + 1) dar x² + 1

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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: Evaluate the integral by using a substitution * x2 dx J Nx2 + 18 3x 2- 18 + 9 In (x + V2 + 18) + C…

A: Solve the indefinite integral by using the substitution method

Q: 5. Determine if the integral is conve 0. exdx -1/2 V1-e 2x

A: Given query is to find integral converges or diverges.

Q: What is the integral of f(x) within the interval [2, 4]? AY 6- O Area = 2.0 O Area = 2.5 O Area =…

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Q: Evaluate the integral -3-2s ds. V-3-2s ds %3D

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Q: Evaluate the integral 169 S. 13 dx 3 x( In x)³

A: Given integral ∫13169dxx(lnx)3. The objective is to evaluate the integral.

Q: 2. In r dr

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Q: Evaluate the indefinite integral: ∫(z−4/5 − z2/3 + z5/4) dz

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: (b)Evaluate the integral directly we-wdw

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Q: Use properties of integrals to evaluate 3 (2æ²) dæ, if j 3 (2a²) 2 j (2*) dæ = *. -2

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Q: Evaluate the integral +2 zp; :- 2 in the two cases: 1) y = {z :|2| = 1}; 2) y = {z : |2| = 3}.

A: We will evaluate it by Cauchy Residue Theorem Let R be the residue then ∫f(z) dz = 2π i R Firstly,…

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

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Q: Using only the definition of RS-integral, evaluate 2 ,2 x* d[x}.

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Q: 2. Prove or disprove that Z, xZ, is integral domain.

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Q: 2- dr Va2 + 1 Evaluate the integral

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Q: [(9)se x². d²+xdx + (x²-n²) y=0_ by substitution x== 1102 at 2 pt souhen Hence show that it has no…

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Q: dr 5. 2 ?+3 2

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Q: x* + x2 + 4 dx. x5 + 8x3 + 16x

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Q: (4 b Prove that 5 foxx dx = K (6-a) using definition of integral, where fø= k [a,b], on

A: Given function is fx=k on a,b. We have to prove that ∫abfxdx=kb−a. Take Left hand side  Use Property…

Q: Sy+ –3-dy у (3–2) 3

A: Our Aim is to find the integral of ∫y+3(3-2)23dy -(i)

Q: 4. Evaluate the integral by interpreting it in terms of areas. •3 (a) |x| dx

A: x→x,      x>0-x,   x<0Given interval is +ve(greater than zero) so x = x

Q: Evaluate integral of dx/x+2 from -6 to -10 Choices: •In 2 •In 3 •21/3 •1/2

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Q: dydr 13. Evaluate the double integral J, J, o x²+7 a, In 10 b. In 10-In 7 а. c. In 11 d. In 11+In 7…

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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: Q/Determine the methods of integrals and discuss the prove one of them with an ехample?

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Q: Q2/Evaluated the integrals v2 1- f– (1-v2 )2

A: The integration of v2/(1-v2)5/2.

Q: The integral of x²Inx with respect to x is; A -(3lnx+1) +C ® (3lnx – 1) +C © 3lnx – 1) +C 3 D -(Inx…

A: Product rule of integration : ∫u.v dx = u∫v dx -∫dudx∫vdxdx dlnxdx = 1x ∫xn dx = xn+1n+1 +C In…

Q: yz dxdzdy -126 -84

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Q: Evaluate the integral a"(2* - 3) "de, 19 by making the appropriate substitution: u = 19

A: The given integral is ∫x3x4-319dx

Q: Evaluate the indefinite integral. dt 6 (t + 13)° + C

A: Explanation of the answer is as follows

Q: 5. Evaluate the integrals using appropriate substitution., a. x*/5+x* dx b. f coszdx os-dx 7x2 +…

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Q: Use tlie kesidlue theorem and colaula re the integral (x-0 (x12)(x-i)(x+i)

A: Consider the given integral. I=∫-∞∞1x-1x+2x-ix+idx The residue theorem is defined as.…

Q: S (e* - ) av

A: Solve the above integration.

Q: S(3x – 2)(x + 1) dx

A: First multiply the expression under Integral then integrate and put the limits

Q: 2. Use Cauchy3 Integral formula, Evaluate the following • I=0 e %3D

A: The given problem is to evaluate the given complex integral over the given contour using cauchy…

Q: 2. Evaluate the integral

A: To integrate

Q: 2 Evaluate the integral of x^3/square root (x^2+4) using a trig sub

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Q: Evaluate the integral. dr V 25 + 2

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Q: Evaluate the integrals

A: We have to evaluate the integral ∫33dt3+t2 We know  ∫dxx2+a2=1atan-1xa

Q: evaluate the integral no u sub

A: Given :          ∫56xdx

Q: Evaluate the integral. V3/2 dr V1- r2

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Q: 17Va – 36 Evaluate the integral: -de

A: Given,          ∫17x2-36x4dx

Q: Evaluate the integral * -In2 2e0 cosh 0 do -In4

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Q: 5/(5x+5x^2+x^3)

A: We apply partial decomposition to calculate the integral.

Q: Evaluate the improper integral .a-2 dz. 1 dr. (4-a)2

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Q: Evaluate the Integral Sec² √r √x dr Njw SYD

A: Given: ∫1832sec2xxdx To find evaluate the given integral.