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

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

A: SOLUTION-

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: Compute the indefinite integral of the following function. r(t) = (5 cost,8 sin 7t,9 cos 3t) Select…

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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: Which of the following integrals are improper? Why?  integral 0 to 1  tan x dx

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Q: Q2 Find the integral for the following : 2- fe-*sec? (ne-*)dx dx 3- JItex dx 1-S; 2x+2x

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

A: Given: i.∫1∞4 sin2xx2+6dx ii.∫01e9t dte9t-1

Q: Evaluate the following Integrals 1 I. dx 1-cos x

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Compute the following integrals: sin x dx -T/2 :/3 |(cos x)(sin? x) dx -n/3

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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 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: #2

A: To find out the integration.

Q: Evaluate the following integrals.

A: Given: I=∫012sin-1x1-x2dx                                              ...1 for evaluating given…

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

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Q: Evaluate the following integrals.

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Q: I. Evaluate the following integrals. · cos³@de 4. S 1-sin® 5. S tan ( – x) dx

A: To Determine :-  The integral  4. ∫cos3 θ dθ1 - sin θ 5. ∫ tan  x4 - x  dx

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: 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: 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: Evaluate the following integrals.

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Q: 3. Evaluate (using appropriate substitutions if necessary) the following definite Integrals. (a) ,…

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

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Q: Consider two integrals: (a) So sin x dx -2пл+1 (b) +1 sin ædæ. Given that n is an integer, which…

A: The objective is to check which integral is greater.

Q: sin xcos x dx 2 X COS

A: ∫sin2xcos2xdx

Q: tan 2x dx 2. S (3+ln cos 2x)6

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Q: Which of the following definite integral has the greatest value? B sin x dx 2+xdx O S 16-xdx

A: We have to find greatest the integral which have greatest value

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 definite integrals.

A: I =  ∫01xsinπx.dx  ................(1)we know ∫abf(x).dx = ∫abf(a+b-x).dx

Q: Find the following definite Integrals : Wir ( i+ sec?x)dx 2. a. X.

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Q: Which of the following is one of the correctIconvenient steps to evaluate| cot-4dx_which will yield…

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Q: sin t ( 10 + COs t)3 7 - sin 4x 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 definite integral : , π/2 3 sinx cos x dx let u = 1 + 3 sin? x 1 + 3sin?,

A: Given,         ∫0π23sinxcosx1+3sin2xdx ;  Let u=1+3sin2x

Q: Evaluate the following integrals: 1. So? 2. cos 2x dx

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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: Evaluate the following integrals /8+tan x dx 1-sin?x i.

A: Note few things.

Q: Which of the following integrals are improper? O " tan xdx dx -dx L2+1 .2 dx -2 x+1 Se*dx None of…

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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…