Question 1 Find the integral: I = (cosaX cosnx) dx a sinan cosnT (A) I : 2a sinan cosnT (B) / a² -n? 4a sina CosnT (an) +n² (an)-n2 4a sinan COS T (C) = (D) / a² +n? (A) (B) (C) (D) Vindows A Moving to the next question prevents changes to this answer.

Q: 1 a) I = S: dx x V4-x2 1 b) I= Sarž dx x2 V1+x2

A:

Q: Question 8 Which of the following is NOT EQUAL to the given integral. tanx There is no correct…

A:

Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

A:

Q: 17. Find the indefinite integral: Te-* dx

A: To evaluate the given indefinite integral.

Q: Question 4. (1) [x³² √x² + 4 dx. X3 sin (In x) X (ii) S -dx. Evaluate the integral: (iii) Choose a…

A:

Q: Question 005: Complete the following question involving Substitution Method. Given the integral re3x…

A:

Q: Question 10 Using the method of Variation of Parameters, the particular solution Y, for the NHLDE…

A:

Q: QUESTION 6 Evaluate the integral in problem 5, using the appropriate trigonometric substitution. OA.…

A:

Q: Question 3 (a) Use an appropriate contour integral to evaluate cos(x) dx 7- sin(x) – 2 cos(x) and…

A: To find - Use an appropriate contour integral to evaluate

Q: Question 16 In (ale) (2-sec2x)emlesec'x sec( 3A – x) What should be the value of A for dx to be…

A:

Q: Question (2): Each integral below has a substitution listed with it. For each integral, in one to…

A: Consider the parts (b), (c) and (d) of question (2), (b) The provided integral and substitution of…

Q: Question 004: Complete the following question involving Integratin by Parts Method. Given the…

A: the given integral is ∫4x*sin5x dx and the substitution information is: u=4xdu=4dxv=-15cos(5x) we…

Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: Question 003: Complete the following question involving Substitution Method. siven the integral…

A:

Q: Question 2 d cos x Find dx In x A. X sin x x In x sin x+cos x x (In x) 1 COs X x In x sin x+cos x D.…

A: To find differentiation  ddxcosxlnx

Q: Ssin dx 32 A COS -5cos 35 cos"()- cos ()• c 32 COS 32 B 32 5sin +2 35 cos COS o -cos"()- cos ()-c 32…

A: ∫sin3x2 cosx4 dx On simplification, we get ∫sin3x2 cosx4 dx=∫2sinx4cosx43 cosx4 dx…

Q: QUESTION 5 Which of the following is not an improper integral? 2 cos x dr 1 dx COS x cos x dr 0. 1…

A:

Q: 5 sin r Question 3 (The Substitution Method for Definite Integrals). Calculate dr. (3+2 cos r)

A:

Q: Question 003A: Complete the following problem involving Basic Integration Find the following General…

A:

Q: Question 3 Calculate the integral: 2x sin(3 x) dx 2 2 a) Ox cos(3x) + sin(3x) + C 2 b) O-x cos(3x) +…

A: Apply integration by parts

Q: Question 5. Evaluate the indefinite integral 2020 (x) tan 2021 (x) dx. COS“

A: Given :

Q: Evaluate the integrals

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

Q: Question 15 1-sine Evaluate the iterated integrals J. J. p2 cose dr de̟ A 1 В) 2

A: ddθ(sinθ)=cosθ ∫rndr=rn+1n+1, for any real number n.

Q: Question 31 Evaluate the integral: A B C D H|m 1 1 13 1|6 sin(3x)cos(3x) dx

A: To evaluate the integral.

Q: dx The integral - tan + C is given in Section 5.5. Verify this a + x? a result with the appropriate…

A: Given: ∫dxa2+x2 = 1a tan-1xa + C To verify: The result with the appropriate trigonometric…

Q: QUESTION 5 Evaluate the integral: S sin?(2x)cos (2x) dx O sin°(2x) sin'(2x) + C 14 O sin°(2x) sin…

A:

Q: (Boas, 2.11.12) In the following integral express the cosine in exponential form and then integrate…

A:

Q: QUESTION 4 witQUTMOUTMOU with respect to r. Differentiate y 3- cosh r 6+ sinhr MO

A:

Q: 5 sin r Question 3 (The Substitution Method for Definite Integrals). Calculate dr. (3+2 cos r)2

A: We use substitution method to solve above integration ..

Q: Question 2 Differentiate the following functions (i) If y= e-t sin 4t, prove that +6+2y = 0. (ii)…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: 8. / (V80 – x² 0.3 cos(1.2x + 1.3) + 5) dx -

A:

Q: Question 4 Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the…

A:

Q: Sræsin(x³/2)dx= cos(x3/2) + C A 2 B) -을 cos(x3/2) +C ©-3/2 cos(x3/2 ++ C) C 2 D /xcos(x³/2) + C

A: Given: Let I=∫x sinx32 dx To Find: To evaluate the given integral.

Q: Question 8 Let y = tan find the differential dy of the function. O dy = e* (x² – 1) sec² \ e*"-1 dæ…

A: As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And ddxtanx=sec2xddxex=ex…

Q: Question 19 Evaluate the integral given. c(2x)tan(2a)dx +C %3D > Next Question

A: To find out the integration.

Q: Question 13 Evaluate the integral J sinh? (2x)cosh(2x) dc sinh“(2x) +C A sinh(2x) +C B 9 costf(2x)…

A: Use the derivative identity, ddx(sinh(ax))=acosh(ax) And the power rule of integration is:…

Q: QUESTION 1 Estimate the integrals of I, both analytically and numerically by using Multiple…

A:

Q: (r+sin 0- cos 0) dr + r (sin 0 + cos 0) d0 = 0

A: (r+sinθ-cosθ)dr+r(sinθ+cosθ)dθ=0 lets rearrange and then integrate

Q: Question 7 5 pts Evaluate the integral using the method of substitution. cos(ln(12z)) Round your…

A: The given integral is: I=∫122cosln(12xxdx Substitute  ln (12x)=t⇒112x(12)dx=dt⇒1xdx=dt  Now, as…

Q: SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п <x< 8п n=1 +

A: The Fourier series of the function fx on -L,L is as follows. fx=a0+∑n=1∞ancosnπxL+bnsinnπxL. Use the…

Q: QUESTION 12 The integral dx can be evaluated using a trig substitution with x+3=2sine. x +6x+13 O…

A: You say to solve the question number 12. So , we will check the problem number 12.  And we will…

Q: Question 170 Calculate f 3 in x.cos x dx. (a) 3sin x cos x , In 3 (b) 3cosx . In 3 (c) 3sin x. In 3…

A:

Q: Question 1. Determine the following integrals: | 1.1. / 2r sin(a² + 1) dx 1.2. ze

A:

Q: Question 16 Which of the following is one of the correct/convenient steps to evaluate -+dx which…

A:

Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.)…

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: Question 13 5 Point sinx sinx +x Cosx - e +e The integral dr may be written as nsinx me +px + qe…

A:

Q: QUESTION 6 Evaluate the integral. Give an exact answer. x?In(2x)dx [Ans] Show your work separately…

A:

Q: Question 13 The integral csc(0.5) dx is equal to A None of the given choices B2ln|csc(0.5x) +…

A:

Q: Question #8 C15: “Find the approximate or exact value of a definite integral using rectangles and/or…

A: