2-7. Basic integration techniques Use the methods introduced in Section 7.1 to evaluate the following integrals. 3x 2. cos (3 + 3) dx 3. Vx + 4 sin 20 3 4. 5. cos² 20 x2 + 4x + 13 x³ + 3x? + 1 dx 6. -dt (Hint: Let u = Vi - 1.) 2t 7.

Q: Se sin 3x dx Using integration by parts, if u = sin 3x and dv = e*dx , %3D what should be du and v?…

A: We know that, The expression for the integration by parts: ∫udv=u·v-∫vdu   Given: I=∫exsin3xdx

Q: Evaluate only four integrals of the following integrals: 1/4 1 dx (i) dx (ii) J √1-9x² sin (3x) 0…

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Q: 4 3 12 2 cos (x2) 3Vz Evaluate the integral|| dx dy dz by changing the order of integration in an…

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Q: 8. Find the general indefinite integral (x³ -2² + x)dr; b) / (2" +-)dr, x > 0; c) (sin(3t) +…

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Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is…

A: Given query is to rewrite the integrand in integrable manner.

Q: a=1 and n-1. Let f(t) = tet SHOW all of your steps of integration clearly.

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Q: The Particular Integral for the Euler Cauchy Differential Equation d²y dy is given by - 5x + 9y = x5…

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Q: B) Use the techniques of integration to evaluate. (Solve 2 only) 3) J tan-ty dy dx 2) (1– x²)5

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Q: 4. .2 + 2x) cos(2x) dx

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Q: ⌠31 (e0.5x + sin2x) dx. use n=4 ⌠41 cosx(0.25x2 + 1.90)dx, use n=3

A: As you didn't mention any question, we will only answer the first parts of these questions. Please…

Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: 3 1 Evaluate the iterated integral 12x -1 0 3 1 °dy dx = -1 0

A: Evaluate the iterated integral.       ∫-13∫0112x2y3dy dx

Q: (4)Evaluate the definite integral (a)[ 1+sin x dx (b) | 2t + cost dt -7/2 5 x + dx (d)[ sec' 0 d0…

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Q: 1. Evaluate the integrals x³e- dx

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Q: 4 dx Vx(1 + x) roper for two reasons: The interval [0, co) is infinite and the integrand h 4 4 dx =…

A: Here we use substitution so simplify the integration.

Q: ull Pure Talk 12:55 PM 90% s3.us-east-1.amazonaws.com 1 | w(w2 + 1)³dw -1 x3 1 dx x2 sin30cos0 d0…

A: ∫-11ww2+13 dw=0, Since ww2+13 is odd.

Q: Q.2// Find (A) f sin¹ (x) cos5(x) dx (B) f 4t³-t²+16 t t² +4 dt (C) Use improper integral to find ²…

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: 6.2.24. Evaluate the integral. using integration by parts integrate 1 to 2 xln(x) dx   I am unable…

A: Use integral by part rule.

Q: 1. a) For 0<x<1, show that /2 1+ x b) Use the estimate in a) and integrate it to prove that 1 1 -dx…

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Q: 17. When we use the integration by parts to integrate * sin-x dx we obtain an expression of the form…

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Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: 3t e2t dt Evaluate the following integrals. 4 Зе + - 5t5/2 a dt - t3 2x cos(9 - x2) dx sin(9 – 2) -…

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Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: 8. Evaluate the double integral. cos 2x.sin y dy dx

A: Solution-

Q: To evaluate (A) (B resti x²cosx dx use integration by parts. What is the expression after the second…

A: In this question, we need to evaluate the given integral using integration by parts.

Q: The integral of the given function | sin 9x cos 4x dx is equal. .... 13 cos(5x) — 5 сos(13x) А. + C…

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Q: 1.0) Find the following indefinite integrals: 1.1) ∫ (5 + x7) (3x2 + x-4) dx

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Q: 1.Evaluate the following integrals and check using differentiation: d5-5t dt 10 0.5t sin(0.5t)_3…

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Q: 11 By reversing evaluate the -3 -9 ffix the orders of integration following integral x cos(y) dy dx

A: Given integral ∫03∫x29 xcosy2dydx The region bounded by  y=x2 , y=9 , x=3 and x=0

Q: a) Find the indefinite integral of the function 1 y = 3t2 + 2e3t +- + 2 cos 3t | b) Calculate the…

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Q: 4.1 Evaluate the integral [3√x √(3√x - 1 / +5 4 + x² expressions after applying the integration…

A: We have to evaluate the integral

Q: 6.3.18. Evaluate the integral. using U substitution integrate (cos^2(x)sin^2(x))dx

A: Hello, there are two functions present in the question. As the first function comes along with the…

Q: 9 In order to evaluate the following integral 1 -√2/cos-¹(√x) dx 1 =- we first use the substitution…

A: Given: I=-∫12xcos-1(x)dx

Q: 3.1 EXERCISES In using the technique of integration by parts, you must carefully choose which…

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Q: Evaluate the integrals: 1- dx TT/2 7cos t sin t dt 0. 2-

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Q: In x)2 To evaluate aX, apply integration by parts twice. For the second application of integration…

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Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: 9/u The evaluation of the Integral of S° sin2x cos4x dx is

A: we have to integrate

Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: 7) Perform the following integration. S(5x* - 82' - 3x' + 2)d = a. b. ſcos' (21)sin(21)dt =

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Q: Evaluate the integral. 6x2 sin AX dx Step 1 To use the integration-by-parts formula u dy = uvV – v…

A: Given:

Q: 2х n evaluating J cos²(2x) Tx using integration by parts, identify the portion of the integrand to…

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Q: 25 2 8 5 cos (x²) 4Vz Evaluate the integral -dx dy dz by changing the order of integration in an…

A: Consider the provided question, We have to find the integral ∫025∫02∫4y85cosx24zdxdydz by changing…

Q: Evaluate the given integrals. 3x?dx 1. S 2х4-1 2 dx 2. S tan x(5+ln sin x) 3. Seš(6– ei)" dz 1 4. S…

A: according to our guidelines we can answer only three subparts and rest can be reposted thanku.

Q: 2.4- Find the Integration of SFex) -dx by Simpson's rule knowing that: i-6 > Use 1.5 3.0 72.0 1.0…

A: Simpsons' rule is given by- I=h3y0+yn+2y0+y2+....+4y1+y3+..... Where h is the step size, h=b-an…

Q: Consider the indefinite integral Ва3 + 21? + 5а + 0 dx x² – 1 | Then the integrand decomposes into…

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Q: 1-2 Evaluate the integral using integration by parts with the indicated choices of u and dv. 5.6 2…

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Q: 1.Evaluate the following integrals and check using differentiation: d 5-5t dt 10 +2.12e- . (a) 0.5t…

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Q: 1. Evaluate the iterated integrals. √27x² (a) [sin - dydx (b) √√x² - y² dydx

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