39. Determine the integral of: S x²e* a. e*(x2 + 2x + 2) +C b. e*(x² + 2x – 2) + C c. e*(x2 – 2x + 2) + C d. e*(x² – 2x – 2) + C 40. Evaluate: S sin* x cos5 x dx 2sin x sin5 x а. sin° x sin5 x 2sin" x c. sin 5 sins x b. 9. 2sin? x sin° x sins x d. 2sin x sin° x + 7 A LA -E

Q: Еxercise: 1- Use the Composite Trapezoidal rule with the indicated values of n to approximate the…

A:

Q: In the integral of x cos 2x dx with limits form 0 to pi/2, what is the indefinite integral? Select…

A:

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

A:

Q: 1 Determine the following integrals: ļ (cos2x+ sin x) dx 1.1.1 .1.2 1.1.3 1₁ Jx Xx+1 √√x²+2x+1 dx…

A: Given integrals, 1.1 ∫(cos2x+sinx)dx 1.2. ∫x+1x2+2x+1dx 1.3. ∫eln(3x)+2x+1dx The objective is to…

Q: Evaluate the double integral of cos(x) with x from 0 to π/4 and y from 4y to π

A:

Q: 7. Evaluate the integral. J CoS X dx 0 1+sin2x

A:

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…

A:

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: 1 To evaluate the integral J dx, we substitute x = 3 tan 0-4. (z²+8z+25)*/2 Select one: O a. True O…

A:

Q: 5. Calculate the double integral f, sin(2x) cos(3y) dA , R = [0, 1/2] x [0, 1]

A:

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

A:

Q: integral of (cos(4pi t) i + sin(5pi t) j + t^2 k) dt

A: Given∫(cos(4πt)i^+sin(5πt)j^+t2k^)dt

Q: х cos 4x dx; и 3D х, dv cos 4x dx =

A: Given that  u = x ;  dv = cos 4x dx and we have to integrate by parts the given integral that is ∫x…

Q: Evaluate the double integral: ∬ 4y/(1+x2)dydx y runs from 1/2 to 2 x runs from 0 to 1

A:

Q: Evaluate the iterated integral. 21 4 (x2 – 2y2) dx dy

A: We need to evaluate the following iterated integral ∫12∫04x2-2y2dxdy

Q: 5 Evaluate the integral 2x cos(xy)dydx 4 0.

A:

Q: -Find Fourier Integral for the function: f(x) = {0 x 0 0 <x < 2 1 ans: f(x) = - " sin2w cos(wx) +…

A: Given function fx=0    x&lt;0 or x&gt;01    0&lt;x&lt;2 So we must have  fx=0    x&lt;0 or x&gt;21…

Q: Choose the most appropriate answer: Evaluate the integral : J(e- 182 + sin 11x) dx -18x e + cosll +C…

A: We need to evaluate the following integral : ∫e-18x + sin11xdx

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

A:

Q: 14. Find the equivalent integral of * S x(x+1) O-f3dx + f 3d x+1 dx OS÷-1# R x+1 01 Of //dx -…

A: Here we have to apply partial fraction.

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

A:

Q: 68. (a) In the integral fx cos x dx, let u = x, dv = cosx dx, du = dx, v = sinx + C1 Show that the…

A:

Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: 15. Evaluate the given integral, V4 – 9x² dx: arc sin () A. x V4-9x2 2 arc sin () x V4–9x² В. + c 2…

A: Giiven: To evaluate the integral∫4-9x2 dxFormula: ∫a2-x2 dx=x2a2-x2+a22 sin-1xa+c

Q: Evaluate the integral 3 2x cos(xy)dydx 2

A:

Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

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

A:

Q: Evaluate the integrals of five only of the following: 1) I = St2 e" dt 2) I = Se-2x sin 2x dx 3) I =…

A: Please refer the attached image for complete solution.

Q: Evaluate the integral / cos (r) sin(x) dx 16 COS using the substitution u = cos(x). ,16 cos" (x)…

A: This question is based on indefinite integral.

Q: Evaluate the integral of x cos 2x dx with limits form 0 to pi/2. (A) -3/4 B 0.75 C -0.5 D 1/2

A:

Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

A:

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

A:

Q: 2. Calculate the following transcendental integrals: a) S² exee* dx X b) S (x²+1)In (x²+1) dx cos…

A:

Q: Step by step

A:

Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

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: Verify Green's Theorem by evaluating both integrals v² dx + x² dy dA ax ду for the given path. C:…

A: This question is related to vector calculus solved in step 2.

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

A:

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: Find the integral of (1 + 2x)e^(-x) dx from x-0 to x--. A. 3 B. 4 C. 2 D. 1 O A B. DI

A: Use integration by parts for solving it,

Q: Evaluate the iterated integral. 6. I (8x - 2y) dy dx | 1

A: Given: ∫19∫0x8x-2ydydx

Q: EXERCISE 20.7 Evaluate the following integrals 2x de (k>1) k+cose de sin' e de .lpl<1 1-2p sin 8+p

A:

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

A:

Q: Match the correct representation of "u" to evaluate the given integrals by the method of…

A:

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

A:

Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu

Q: Evaluate the integrals in Exercises 9–12. 4 cos (x²) dx dy 2y 9. e dx dy y/2 10. 27 sin 7x² -dx dy…

A: Given:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.