You found that the reduction formula of a certain integral is In = a" sin 2x + nx"-1 cos 2x – n (n – 1) In-2 and that I1 sin 2xWhat is I3 ? 1 3 sin (2æ) +a² cos (2æ) + sin (2æ) 4 1 3 3 sin (2a) – a² cos (2æ) + sin (2æ) CoS 4 1 3 3 sin (2a) +a² cos (2æ) – sin (2æ) - 4 3 3 sin (2e) –a cos (2xr) – sin (2)

Q: 2 Find [f(x) + 2g(x)]dx if [f(x)]dx = 5 and 1 [g(x)]dx = -3. 1) In order to evaluate this integral,…

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Q: show that: 1/2 1/2 im N-1xP 2(N-1)e (IN-1-20) + - IN-1 dIN exp lim N0002nhis 2nhi(N-1)e) h2e exp…

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Q: To treat the integral -24(2x + 1)2 dx as a constant multiple of one of the form u"u' dx, we let n =…

A: the objective is to find the given integral

Q: Use the appropriate substitution to evaluate the following integrals: (2 1 A 3(2+ cos t)3 + C -1 + C…

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Q: Evaluate the integral. S 20x cos x dx Select one: O A.80 sin. 1 40x cos + C O B.20 sin n1)x+ 40x cos…

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Q: Evaluate the integral 5a2 - x+27 da. (x2 +9) 5x3 x2 + 27z) · In|r(x² + 9)|+ C 2 3 In |피 + 2z In |2…

A: Topic - indefinite integration  Note- as per our guideline if more than one question uploaded only…

Q: Evaluate the following integrals Li l2l e(1+x²) dx i.

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Q: x³ + 6x² + x +2 fx-1 ax + In{(x + 1)*(x² – x + 1)| +- 2 Tan Ve The resulting integral of -1 + C,…

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Q: 1 6. Evaluate the given integral using suitable substituion COs(V도+ 3) dr

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Q: ₁√x³ √4-x² dx. if we let z = √√4-x², which of the following integrals is correct using rationalizing…

A: The given integral,        ∫x34-x2dx

Q: For cach pair of definite integrals in Excrcises 13-18, decide which, if either, is larger, without…

A: 13. both are equal since the area covered by cos is same in both the region. 14. Question not…

Q: The result of the integral 4 / (x - 1)(x + 1) is equal to -dx Select one: O none of these. ○ In…

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Q: : cos'x dx to Which of the following is one of the correct steps to evaluate obtain the desired…

A: Here, we have given an indefinite integral in which  we have to integrate a trigonometric function.…

Q: 17. Use the theory of residue to evaluate the following definite integrals 2 de (2) / 2+ cos 0' cos…

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Q: Evaluate the indefinite integral. Sa V1 - a? dæ cos° 0 – cos 0 +C 3 - 5/2 (1-22)이2-3 (1- 22)이2 +C. |…

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Q: Solve the integral: A In/1+ B -In|1+ x 5. 1 3X + C + C 5 x X + X x dx

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Q: 9-34 Evaluate the integral, if it exists. tb (1)nia 9. ² (8x³ + 3x²) dx 11. f' (1-x) dx 13. f³√x (x…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first part.

Q: You found that the reduction formula of a certain integral is In = x"+2e2= - (n + 2) In-1 and that 1…

A: As per our guidelins we can solve only 1 question. The next question can be reposted.  Here we have…

Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: Match the integral expression on the left to an equal expression on the right. (cos(x)- Prompts…

A: I am attaching image so that you understand each and every step.

Q: To treat the integral -44(2x + 1)-2 dx as a constant multiple of one of the form u'u' dx, we let n =…

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Q: 6. Evaluate following definite integrals: S(3x2 +2x – 2) a. b. (3x + 2VA)

A: Given  a)∫15(3x2+2x-2)b)∫49(3x+2x)  Let us evaluate the first integral (a)let…

Q: (2) Compute the following integrals. /4 (a) sin (4r) cos (4.r) dæ. (b) cos(ka)e-lz dx, Hint:…

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Q: Find the indefinite integral. 4x2+2x-1 d.x none of these Omz + 1| -31m|z미-글+C o+ Inz* + =*|+C In a+1…

A: Given: I=∫4x2+2x-1x3+x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And…

Q: 15x²x³43x - 19 can be rewritten as (x + 1)²(x² - 6x +13) Ax + B C D Slax ² + + lax² + bx+c (mx + n)t…

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Q: 1) Find the integrals: i) i) SF Inx dx 4-X2

A: Part i          ∫x2-14-x2dx

Q: Evaluate the given integrals. 5. S(1 – cos 0) csc²0 d0 -

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Q: Consider how we can evaluate this integral using u-substitution: x S dx. √2x+1 If we let u = 2x+1,…

A: This question can be solved by integration by substitution.

Q: The integral of sin2 3xdx is x 1 -x +A + C, What is the value of A if x =-. 4 O -1/12 O 1/12 O 1/18…

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Q: The integral of the given function sin²2x cos 7x dx is equal sin 7x sin 11x sin3x А. 14 + C 12 44…

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Q: ** The definite integral " - 1/4 • 1/4 tan-1x² + /x²+ 1 Cosx +2 dx is equal to A 1 • T1/4…

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Q: If the integral of x²dx V(9-x²) (0 – →sin 20) + C. What is 0? - -1 O 3Sin (x) O Cos" (3x) O Cos' ()…

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Q: Evaluate the integral using the given substitution. SV cos (2-7) dx Select one: 3/2 sin (x - 7) + C…

A: topic - indefinite integral

Q: 2. Show that 8(x²-a²)= 8(cos - cos') = 3. Evaluate the following integrals, Is = h₁ = √dr 8 (2²-3x +…

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Q: 11. The integral of an(In|4x-12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. 2 С. 4 D.

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Q: Q1 - Find the reduction formula for each of the following integrals iii. In = S x" cosh2x dx

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Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx (3e)3+ cosh2x A + C 2ln3 (3e)3+ cosh2x +C B 2 +…

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Q: 1. Find the following indefinite integrals (any 4) (2/x* - 7x' +10e* – 1)dx (x* + 1)e* iii) dt +3x…

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Q: Evaluate the integrals ∫(2θ + 1 + 2 cos (2θ + 1)) dθ

A: To evaluate ∫2θ+1+2cos2θ+1dθ

Q: Select from the subsections, the one that corresponds to a step of the solution procedure of the…

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Q: 5. Evaluate the following integrals3 sin ttZ dz C: İz-il 471 =D2 ans: C. 3. coshz -27 ans : Icz²3iz

A: By residue theorem, we can solve these problems.

Q: 2 Find fx) + 2g(x)]dxif / F(x)]dx = 5 and / [g(x)]dx - 3. 1) In order to evaluate this integral, use…

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Q: Find a formula involving integrals for a particular solution of  D.E y^‴-3y^″-y^'+3y=sect

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Q: Evaluate the integral V16 – x2 O A.8 sin-1(프) - 특V16-22 +c O B. sin-1(플) + c O C.8sin-1(플) - n. V16-…

A: Option (a) is correct.

Q: THIS BE SOLVED ANALYTICALLY? SO, HOW? (a=0.75 STILL) dy=ay (1-2y). 6y³ - dt 4y³+5 SET UP THE…

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Q: You found that the reduction formula of a certain integral is In = 180 (13x" sin (13x) + næ"-1 cos…

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Q: 8. Find a recursion formula for the family of integrals I (n) = r I(1 x" sin x dx that starts with…

A: Given a family of integrals, I(n)=∫xnsinx dx

Q: 5. Evaluate the following integrals 3 sin #Z dz, c 1z-il=2 24 -4 ans: 3 co shz

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Q: A. B. Evaluate the following integrals using substitution method: (³-1) ²/3 √2 5.² 0 √r sin (1 + x²)…

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