The value of the improper integral 6 x? e-z dx O 2e-1 6e-1 6e-1 - 2e-1 -

Q: r² (x²– 1)(x² + 1) , What is the resulting value of the definite integral dx? х-1 O 33 1 + 4 15 O 31…

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Q: te the improper integral if it exists e'dr: .1 e.2 -e.3 0 The improper integral diverges 4 O

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Q: Evaluating the integral | (2.x* +e* –-)dx gives: O A. 2 +e* – 2 In |x| +c - O. 4.x² +e* – 2 ln|x|+c…

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Q: evaluate the integral by following the steps given.

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Q: dx Using half-angle substitution, the integral reduces to 3+ Scosx dz A dz B dz 422-1 2 dz D 322+…

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: the indefinite integral re (a) 2xe +3x e* +C (b) et +C (c) 3 x3 +1 +C 1 (d) +C 3 (e) None of the…

A: Taking up the given Integral which is mentioned below:-∫ x2 ex3 dx -(i) We will solve equation (i)…

Q: satis ties the given integral. tind the derivanive of yat (0,0) e de =xy (0.0) dy

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Q: Evaluating the integral 1 1 -dz, s(0,1) (z – a)(z – a¯!) prove that for any a E (0, 1), dt 1 + a? –…

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Q: dx Fa) Evaluate the integral z In(2x) using the substitution u = In(2.x). dx |r In(2ar) +C b)…

A: Topic = Integration

Q: 2. The value of the integral in terms of u is? 2u³-21n|u³+1| + C 2u³-3u² +6u-6ln|u + 1| + C 6u+…

A: We know that integration of xn is xn+1/n+1.     Here i attached the solution of this question.

Q: Related integrals Evaluate each integral. - x - y)dr dy ST 14 - x - y|dx dy a. b.

A: Hey, since there are two questions posted, we will answer the first question. If you want any…

Q: b2 a? 2 Use Jx dx a<b, to evaluate the integral x dx. 2 2 a x dx = 2 (Type an exact answer in…

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Q: N/= (2+V1-x²)dx= %3D Hint: interpret the definite integral as an area. 4+ TI+8 2+ I 4 O 4 2+ T

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Q: e a computer algebra system to approximate the iterated integral. (Round your answer to three…

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Q: cosx dx What is the form of the given integral divided into simple fractions? (sin x-sin?x) A) S (…

A: Use the method of Substitution for sinx=v  Then cosxdx=dv

Q: 5. In antidifferentiation, the formula § x" dx + Cis valid if? %3D (n+1) А. nER В. п# 1,п€ R С. п€…

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Q: 42–45. Symmetry in integrals Use symmetry to evaluate the following integrals. /4 r/4 42. tan x dx…

A: Given: 41.∫-π4π4tanx dx

Q: S For x1/2 dx and using the substitution = x1/2, the resulting integral takes the form: x-x3 -du S-…

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Q: Evaluating the integral | (2x +e -)dx gives: 4 +e* – 2 ln x +c O A. 4x² +e* – 2 In|x|+c O B. x* +e*…

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Q: Q32] evaluate the Cauchy principal value of the given improper integral. dx (x² + 1) (x2 + 9) 1 dx…

A: These are multiple questions, i.e., the question post has two or more unrelated questions. As per…

Q: Naluate integral foin+c)dt 3.

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Q: 2x -dx e* +1 Evaluate the integral of A e*- In(e*+1) +e B '+ In (e* + 1) + c © e*+ In(e*+1) +c D In…

A: Given problem:-

Q: Evaluating the integral In(x³)dx, where x > 0 yields: x In(x²) – 2x + C 2x In(x²) – 4x + C O the…

A: Use integration by parts.

Q: Which integral represents the length of the graph of y = xe over the interval [0, 2]: Select one: a.…

A: Arc length of the curve:…

Q: 5. S'dx x In x A. B. xlnx C. Inx D. x

A: None of the option is correct.

Q: Evaluate the integral. S- 1- 2x dx O A. -2/1- e2 +C O B. sec 1(eX) +c Oc. e* sin -1(e*) +c O D. sin…

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Q: B)Evaluate the integrals: i) √1-x2-x²-y² ii) -² ²-²-² dz dy dx. xe dy dx.

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Q: S- S- °S- S For x 1/2 x- U U 1-u4 4u dx and using the substitution -du -du -du 4u √4-(24²) 2 -du…

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Q: Which one is an improper integral? O 6 sin(x-5) x-5 S₁º O none O 6 sin(x-5) x-3 O S 6 sin(x-5) x-7…

A: Improper integral:- An improper integral is a definite integral that has either or both limits…

Q: 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

A: We have to solve

Q: g(b) Use the Substitution Formula, f(g(x)) g'(x) dx = f(u) du where g(x) = u, to evaluate the…

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Q: z? +2z+3 -dz Evaluate the integral (z-6)(z² +4)*

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Q: 15. Evaluate the integral: sinz' dx А. 2л сos л? + с С. 1+ С В. xsinл* + С D. 0+C

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Q: sec 2x In evaluating the integral dx, using the appropriate formula, the du = M. V1+tan 2x •1/2…

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Q: ‹S- A S Ⓡ /- © /- S- D For dx and using the substitution = x1/2, the resulting integral takes the…

A: Just use the substitution and find the required integral. Option (B) is correct.

Q: dx 2. Find the integral x²(x+1) In (***) + C b. In (***) - +C 1+ C c. In (***) ++ c d. None of the…

A: Here we have to find the integral

Q: (2- sec?x)eln (afe°sec³x sec(3A – x) What should be the value of A for dx to be integrable using the…

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Q: The value of the iterated integral S S. S Tsin(ry)dydrdz= ... Select one: O A. None of these answers…

A: The triple integral I=∫ab∫g(z)h(z)∫p(x,z)q(x,z)f(x,y,z) dydxdz is solved as Integrate the function…

Q: 1+x2 n = 10 Approximate the integral use the Simpson 1/3 Rule 4 dx n = 10

A: Here f(x) = 11 + x2h = b - aN = 4 - 010 = 0.4 The value of table for x and y x 0 0.4 0.8 1.2 1.6…

Q: Evaluate the iterated integral.   6   2   x 2ye−x dy dx   1

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Q: The value of the improper integral [e*dx= а. 1 b. 0 C. -1 d. 00

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Q: Evaluating the inmproper integral ze2 dz gives the answer A) 3/4 B) -3/4 C) 1/4 D) –1/4 E) 2/3 F)…

A: Consider the given integral. Calculate the integral.

Q: Evaluate the integral. dx 7 X> 4 V16x? - 49 Which substitution transforms the given integral into…

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Q: ·S- For x 1/2 dx and using the substitution=x1/2, the resulting integral takes t U -du 1-u² 4u 4-4²…

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Q: (b) Find the value of the following integrals: z-1 1- (z'+z-2)" z = 3i, z 2. dz, y is the triangle…

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Q: K O O Given the integrals I, J, K and L, where 3 dx = 6²° 3 .00 dx x + 2' O 1 = = [₁*√x- √x-3 dx, L…

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Q: The value of the integral Select one: a. 3 b. None of these d. / [1² 17/12 2y³ dx dy is

A: Evaluating the definite integral

Q: 1. Which of the following integrals is improper? Explain your answer, but do not evaluate the…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Q: Evaluat the integral. Q₁ is's ex dxdy 3y +²

A: Here we have to find the integral.

Q: INSTRUCTIONS: EVALUATE THE FOLLOWING INTEGRALS - e* 1. dx e* +e-z -10 2. dy e+ 3. 4.r sin(4r + 5) dr…

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