de 63. 64. e" cos u du e2 + 1

Q: Use reduction formulas to evaluate the integrals in Exercises

A: Evaluate the following: 45. ∫4tan32x dx46. ∫8 cot4t dt

Q: Evaluate the integral. * T/3 3 sec 0 tan 0 de In/4

A: Given that the integral is ∫π4π33secθtanθdθ. It is required to evaluate the given integral…

Q: Evaluate the integrals in Exercises 69 : (2r – 1) cos V3(2r – 1)² + 6 -dr V3(2r – 1)2 + 6 69.

A:

Q: Evaluate the integrals in Exercises 25–30 by using a substitution prior to integration by parts.…

A:

Q: Calculate the iterated integral A 67 5x cos y dydx. 1 2n 5

A: Explanation of the answer is as follows

Q: Evaluate the improper integrals in Exercises dr 53. 54. In x dx 6/

A: since you have posted multiple questions , so I'll solve first one for you , for rest question's…

Q: Evaluate the Type I Improper Integral: re" da.

A: The Type I Improper integral ∫-∞0xexdx can be written as ∫-∞0xexdx=limn→-∞∫n0xexdx

Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

A:

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4- 3.…

A: Given:

Q: Evaluate the integrals in Exercises 37–44. 37. Jau. cos x sin x dx sin³ x cos“ x dx 38. tan“ x sec?…

A:

Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

A:

Q: Use reduction formulas to evaluate the integrals in Exercises 41–50. Ssin' 2 de 8 cos“ 2nt dt 42.…

A: Dear student, Since you have asked multiple questions in a single request, we will be answering…

Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…

A:

Q: Evaluate the integrals in Exercises

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the integrals in Exercises 45–76. 2(cos x)-1/2 sin x dx (tan x)-3/2 sec²x dx 45. 46. (20 +…

A: Hello thank you for the question. As per our guidelines we are allowed to answer one question. So,…

Q: Evaluate the integrals in Exercises: -1/3 6 dx VI + 9x? 5- TT cos x dx Jo vī + sin²x Vi + sin²x 6-…

A:

Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: Evaluate the improper integrals in Exercises

A: Solution:Given59.∫0∞ x2 e-x dx60.∫-∞0 x e3x dxFormula:(xn)'=nxn-1eax'=a eax∫eax dx=eaxa+C

Q: Evaluate the integrals in Exercises 51–56 by making a substitution (possibly trigonometric) and then…

A:

Q: Which of the improper integrals in Exercises which diverge? converge and de 63. 64. e" cos u du Vo +…

A: 63. ∫6∞dθθ2+1=lnθ2+1+θ6∞=∞ Since the value of the integral is infinite, therefore the given integral…

Q: Evaluate the integrals in Exercises

A: 47. ∫sech2x-12 dx48. ∫ csch25-x dx

Q: Evaluate the integral in terms of u. sinh u• du = + C %3D 3.

A:

Q: 1) э бирорце f a ad да ore integralbl on [a,b]. Show that of -g is also integralible салоз.

A:

Q: In Exercises 45 and 46, both substitution and integration by parts are used to determine the…

A: 45. ∫exdx46. ∫11+xdx

Q: Evaluate the integrals in Exercises 45. tanh dx 46. coth de

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

Q: In Exercises 27–40, use a substitution to change the integral into one you can find in the table.…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: Evaluate the line integral by the two following methods. dx + x2 Cis counterclockwise around the…

A:

Q: In Exercises 45–48, calculate the integral, assuming that •5 .5 f(x) dx = 5, 8(x)dx 12

A: Given: ∫05fxdx=5, ∫05gxdx=12 To evaluate: ∫052fx-13gxdx Solution: We know that, ∫fx+gxdx=∫fxdx+∫gxdx…

Q: Compute the given improper integral. Enter the exact value of the answer. 7 In(4x)dr 0,

A:

Q: de 1+tan 0 k/2

A: Let I=∫0π2dθ1+tan θ      I=∫0π2dθ1+sin θcos θI=∫0π2cos θ dθcos θ+sin θ     ....(1)Using property…

Q: Eveluate the integrals in exercises (a-b) x 5-x cos (x+

A: As per our guideline we are supposed to answer only one question you can repost other questions in…

Q: 7. 8 sin* x dx

A:

Q: Use the form of the definition of the integral given in Theorem 4 in section 5.2 to evaluate the…

A: First integrate the function x2+7 with respect to x using the power rule of differentiation.

Q: Evaluate the integrals in Exercises 2. [w- 2 1. / x(x – 3) dx (x² – 2x + 3) dx 3 dx dx 3. 4. x299 (x…

A: Note:- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1. Evaluate the following finite integral using the theory of residues 2n sinx 13 — 5сosx Please…

A: Given integral is∫02πsinx13-5cosxdx

Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: 1 -) Prove the existence of the improper integral 1 (In x) sin – dx -

A:

Q: calculate improper integral Poorreligggms ecosemberererii wemer- J $in I + CO8IC Vsinx - CasI paul:

A:

Q: Evaluate the integrals in Exercises 23–26. TT 23. cos (x + y + z) dx dy dz 0 Jo Jo -In 7 cln2 cIn5…

A:

Q: 18- Evaluation of the integral In i dt

A:

Q: Evaluate the integral.  integral  t  3sin 2  t dt

A: To evaluate the integral: ∫3sin2tdt. We know that, sin2x=1-cos2x2 Therefore, using this formula,…

Q: Compute the indefinite integrals. 15e" dx E nolis ISO 29unim 08 aim 8 bue fogr vos irs nibuloni) ag…

A: ∫ 15exdx=15·∫ exdxUse the common integral:  ∫ exdx=ex=15exAdd a constant to the solution=15ex+C…

Q: 2. Use the Fundamental Theorem of Line Integrals to evaluate fe F.dR, where F(x, y) = (x²y? –…

A:

Q: Evaluate / F. dr using the Fundamental Theorem of Line Integrals.

A: In this question, we used the fundamental theorem of vector calculus. here first we prove the vector…

Q: Evaluate the Foll aning integrals a) 32ペ-T Ax b) CSCXXX -1/4 TY3 Sinx よ× /3

A:

Q: 5, set up the appropriate iterated integrals in rios for I f dV on the indicated domains.

A: Step:-1 Given that  The equation of tetrahedron is z = 4 -2x -y⇒2x + y+z =4 ---(1) so, bounds or…