Consider the following integrals 00 4 sin? x i. dx x² + 6 e9t dt ii. e9t – 1 Mark the correct one for the integrals.

Q: Evaluate the following integrals. Show the solution. 1. S csc? (7x + 5) dx 2. fx? sec (4x³ + 9) dx…

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Q: Simplify the following expression d/dx of the integral from 0 to x2 sin(t3)dt

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Q: Use an appropriate substitution to show that the value of the following definite integral has value…

A: SOLUTION-

Q: Consider the following integrals 4 sin? x -dx x2 + 6 00 e9t dt i. e9t – 1" Mark the correct one for…

A: Step:-1 Since, we know cos2x = 1- 2 sin2x⇒2 sin2x = 1 - cos2x An integral is called convergent if…

Q: e) TT/2 cos x In(sin x) dx t/4

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Q: Compute the following integrals. 1 (i) Ss(0.2) sin*(e) cos(2) dz.

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Q: Use the Table of Integrals to evaluate the integral. T4 - 9 sin e sin 20 de 4 – 9 sin 0 |

A: We use substitution to integrate the given function.

Q: Evaluate the following integrals (i) So V1– cos 2xdx

A: Since there are multiple questions posted, we will answer the first one (i). If you want the…

Q: Evaluate the following integral using the Beta function: CT/2 sin? 40 cos? 20d0 COS

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Q: Q2 – Evaluate the following integrals. i. S(sin(4x) + cosh(3x))dx

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Q: 1 sin Tx cos TIx dx 0,

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Q: Evaluate the following integral using trigonometric substitution. 7/2 1 0 dx 2 (4x²+1) ² What…

A: I have stated the used formulas in the solution

Q: Consider the following integrals 9 sin? a 00 i. 2² + 7 •1 ii. e5t dt e5t – 1 Mark the correct one…

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Q: (d) Ꮭ /2 sin 6 er cos 0 r²dzdrdo

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Evaluate the following integral using the Beta function: •T/2 sin? 40 cos? 20d0 0.

A: Consider the provided integral, ∫0π2 sin24θ cos24θ dθ Evaluate the above trigonometric function.…

Q: Approximate the following integrals using the Trapezoidal rule. c0.25 (cos x)? dx b. x In(x+ 1) dx…

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Q: Evaluate the following indefinite integrals. sin? 5x cos? 3.x dx

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Q: Evaluate the following integrals TC 2x a) -e + sin dx V3x 0. 3. cot(-2x) csc?(-2x) dx b) 7.

A: (a) I=∫0π53x-e+sin-2x3dx =∫0π53x dx-e∫0πdx+∫0πsin-2x3 dx  ∵∫(u+v) dx=∫u dx+∫v dx…

Q: Consider the following integral: dx I : a. Use the substitution u = x - 1 to show that I = sin(2x –…

A: Indefinite Integration

Q: Consider the following integrals 5 sin? x i. x² + 6 est dt ii. e3t – 1

A: We have to use comparison test here.

Q: Consider the following integrals • * 5 sin? æ i. - dæ x² + 6 e3t dt ii. . est – 1

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Q: Which of the following integrals are improper? (Select all that apply.) dx 5х — 1 dx 2х — 1 sin(x)…

A: An improper integral is a definite integral in which the limits approach a constant, or,…

Q: Evaluate the following indefinite integrals: +3.7 4. da 6. 12 sec 0 tan 0 d0 7.

A: Explanation of the answer is as follows

Q: Q1: Evaluate the following integrals by using a substitution to reduce it to sec X dx 1 standard…

A: We have to use substitution method.

Q: A. Evaluate the following integrals: 1. sin 'xcos x dx

A: Given: I=∫sin7xcosxdx   ....(1)   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Evaluate the following integrals S, 5v – 3) (e-y*2 sinhy) dy а. b. 8(x + 1) In(sinx2*) cosx dx

A: We have to define the given Delta function and find the points in which it is non zero in the given…

Q: Evaluate the following integrals.

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Q: Evaluate the following integrals. (a) / (csc0)(1+ sin² 0 + sin 0 cot² 0) d0 (b) /: (e) / dr VI-2r2 +…

A: Part(a) We need to evaluate ∫csc θ1+sin2θ+sinθ cot2θdθ Consider: ∫csc θ1+sin2θ+sinθ cot2θdθ=∫csc…

Q: dx 4-e4x S sin 0 V1 – cos 0 d0

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Q: Which of the following is one of the correct/convenient steps to evaluate cot-4dx which will yield…

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Q: I. Evaluate the following integrals. 4. cos*ed@ 1-sin® 5. S tan (; – x) dx

A: ∫cos3θ dθ1-sin θ Let I=∫cos3θ dθ1-sin θ        =∫(cos θ. cos2θ) dθ(1-sin θ)       =∫(cos θ)(1-sin2θ)…

Q: 1. Evaluate the following definite and indefinite integrals. a) St sec2(t?) tan*(t²) dt

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL  BE ANSWERING ONLY THE FIRST…

Q: 1/3 13 sin t dt cos? t

A: Find the given integral

Q: Q1/ Evaluate the following integrals: (a) / sin' cos를 dx. (b) S dx . (e) Sr² G- 1) dr .

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

Q: Evaluate the following integrals: i. Se- cos(20)de ii. dx Va+100

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Q: Consider the following integral (r+ 2)²dx J V5 – 4x – x² After making the trigonometric substitution…

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Q: Consider the following. 0.75 +² dx V9-16x² 3 Let x = sin(0) and determine the following. 4 dx = de x…

A: Given I=∫00.75x29-16x2dxI=∫00.75x232-(4x)2dxLet  x=34sin(∅)Differentiate dx=34cos(∅)d∅As x=0 →∅=0…

Q: Evaluate the following integrals. When using substitutions, be show to show them explicitly. a) + 5…

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Q: (d) Find the following indefinite integrals. xer (i) 1+e? xp. (ii) | cos (2r) sin (2r) dx

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Q: Calculate the following Integrals: sin(3x) sin(a x)dx, a e R ahd j sin (3x)· e*a*dx, aeR, i the…

A: The objective is to calculate, ∫0∞sin3xsinaxdx It is known from trigonometry that,…

Q: Evaluate the following integrals: 1 + 6x ) dx a) u – 2u? b) du cos(Va) dx (Hint: use u-substitution)

A: We have to evaluate the definite integral in part (a) and indefinite integral in part (b) and (c)

Q: To evaluate the integral | x sin(x2) dx we use the substitution O a. x= t O b. sinx =t O c. sin x2…

A: Explanation of the solution is given below....

Q: e" cos(e“)dx

A: Let I=∫0∞excosexdx  Put   ex=t⇒exdx=dt When x=0, t=e0=1 When x=∞, t=e∞=∞ So, by substitution, the…

Q: solve the following integrals:- dx |1-x² (1) J (2) Sx sinždx (3fdr (++x^)x^

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Q: L sin-1 x dx

A: We need to calculate the integral: ∫01sin-1x dx This can be done as follows:

Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

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Q: cos“ x sin x dã

A: In some cases, an integral can be simplified to a standard integral with an appropriate…

Q: Evaluate the following integrals. Tt/42 cos x dx e* 2 cos а. S dx V1-9x²

A: We have ∫0π42 Cosx dx Now, ∫0π42 Cosx dx becomes  ⇒2Sinxπ40                         as ∫Cosx…

Q: Q1/ Evaluate the following integrals: (a) S sin³ cos dx . (b) Ja dx . (e) S r² (- 1) dr .

A: We have to find the value of the integrals given.  Note- since you have posted multiple independent…