-10 10 X -10 Use the substitution formula to evaluate the integral. 214 9 tae 277 18) 3 cos2 x sin x dx 18) Tc/3 T/2 19) COS X 1O e dx 7 0 (2 + 5 sin x)3 Зп/4 20) (7 + cot 0) csc 2 0 d0 T/4 niled 5/20 21) 8 - X dx VX 1 Find the area enclosed by the given curves. 22) y 2x - x2, y = 2x - 4

Q: Find the general indefinite integral. (a)∫(7−13sin(x)+9cos(x))dx (b)∫(ex+3x−11−x2)dx…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: a) Evaluate the Rollowing integrals 2) sinrde 3)

A: Answer and explanation is given below According to guidelines,i will provide answers of first three…

Q: Describe strategies for solving the types of integrals given in Exercises 8–18. | cos* x dx, k odd |…

A:

Q: 2- Evaluate the integrals in Exercises 7- 8- 9- In 9 Son 24/2 In 4 S dr [ 21 e ² dt ex/2 dx

A: To evaluate the given integrals.

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

A:

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Jizl=1z² sinh z Where 0 < |z| < T.

A: Image is attached with detailed solution.

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

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Q: Evaluate the integrals: 1₁ = - S using Second-order Gauss quadrature. O I₁ = 3.1416 12 = 1.5708 1₁ =…

A: Second - order Gauss quadrature formula:…

Q: 1. One of the following is an improper integral CA In 3 cIn 2 dx xp 4 – ex 2x + 1 JIn 0.5 ' In 2 dx…

A: I am attaching image so that you understand each and every step.

Q: 2. Use Cauchy's Integral formula, Evalnate the following. • I= 6 Sin4Z :(Z-4)3 IZ1= 3 I = . tanttz…

A: Given

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: 2. Evaluate the Integrals using the Fundamental Theorem of Calculus. 1. S/4 cos x dx π/4 2. ¹₁ sec²…

A: First I have written the Fundamental theorem of Calculus, using it for given integral and find its…

Q: 2. Evaluate each of the following line integrals in two ways*. F (x, y) = (2x – cos y) i + (x sin y)…

A: 2. (a) Directly: The equation of the curve C1 is x-4+y5=1( intercept form), or, y=54x+5. The…

Q: 2 3 let (4-x2) 2 dx , write the integral by using Beta function 0. 1 5 8 B 22 .a 1 3 8 B 2 2 B 3 5 2…

A: Substitute x22=t in the integral:  ∫024-x23/2dx=8∫021-x223/2dx…

Q: Evaluate the integral. n/2 | [2 cos ti -3 sin 5t j+ sin? 3t k] dt 0. n/2 | [2 cos ti- 3t k dt = cos…

A: Integrate

Q: 19. fy/6 + 4y – 4y² dy

A:

Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

A:

Q: 6 In x Evaluate the iterated integral given that the evaluation of the inner integral is 7x 3 In x…

A: ∫1e∫1e23lnx7xydydx

Q: 0; x 0

A:

Q: z'sin3z Evaluate dz with C: -2 using Cauchy's integral formula

A: *concept:- Cauchy Integral formula.

Q: 59-64 Use Property 8 of integrals to estimate the value of the integral. x'dx 60. | Jo x+4 59. dx…

A: ∫xn dx = xn+1n+1 +C ∫tan x dx =ln sec x+C

Q: Evaluate the integral. 7 7 √49-x² ILL 1 /49-x² (x² + y²)1/2 dy dx dz =

A:

Q: 11. Consider the following integral: 3r/2 1- Ssin(5x +1)dx 0. (a) Evaluate the integral…

A:

Q: Q3/ Evaluate the integrals : ( choose four only) 1. r cos v S cosv 2- S- dx Va sin V 3- f(s +2s²-5s…

A:

Q: 9. Find the indefinite integral. 1 36+ (x – 4)2 X -4 arctan 36 +C a. 36 オ-4 b. 36 arctan 36 1 x-4 +C…

A: (9) Given: The integral is  ∫136+(x-4)2dx

Q: Evaluate the iterated integral. 7 8 (x² + y² + z²) dx dy dz -6 0 0 7 8 (x² + y² + z² )dx dy dz =

A: Given that: ∫-66∫07∫08(x2+y2+z2)dxdydz

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: In this question, you are asked to investigate the following improper integral: (х-3) -15 10.1…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0&lt;z&lt;π…

Q: Evaluate the integral. 2 | 7t sec -'t dt 2113 | 7t sec - 't dt = 2113 (Type an exact answer, using t…

A:

Q: Consider the integral 2 6z² In(z) dz

A:

Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

A:

Q: 2. Show that 8(x²-a²)= 8(cos - cos') = 3. Evaluate the following integrals, Is = h₁ = √dr 8 (2²-3x +…

A:

Q: What is the integral of f sin² x cos² x dx? cos(z) sin³ (2) cos(z) sin(z) + 4 4 ○ sin(4z)+4z 32 +C…

A:

Q: Evaluate the iterated integral. 5 6 7 ||| ? +y² + 2) dx dy dz -5 0 0 5 6 7 | || (1²+y² +²)dx dy dz =…

A:

Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.

Q: Find the integral ſ cos³0 sin 0 d0 . Tentukan integral f cos³0 sin 0 de. 1 cos*0 + C 4 1. O 1 -coste…

A: Let's find.

Q: You found that the reduction formula of a certain integral is In = a" sin 2x + nx"-1 cos 2x – n (n –…

A:

Q: Transform Bessel's equation x²²y + xdx+(x²-n²) y=0 by substitution x== souber moitops navig Hence…

A:

Q: Consider the integral  ∫17⋅x⋅cos(8⋅x) dx Which of the following choices of uu and dvdv are…

A: The given integral is,∫17xcos8x dx

Q: 5. Evaluate the following integrals3 sin ttZ dz C: İz-il 471 =D2 ans: C. 3. coshz -27 ans : Icz²3iz

A: By residue theorem, we can solve these problems.

Q: Q.1 Evaluate the given integrals using part I of the Fundamental Theorem of Calculus. [3 Marks] i.…

A: You need to find the integral of the given functions using the fundamental theorem of integration.

Q: Evaluate the integral. 1 8 dt V15-21-? - 1 OA. 6 В. O C. 4 D. 3" O D. co fm

A:

Q: 1. Rules of LDef nite Integrals: 12 a) b) rpx 12 12 f(x)dr 4, find the If f(z)dr = 12, " $(z)dz = 6…

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Q: ∫(−2x2+6x−6)dx   Select the correct answer below:   a. 2∫x2dx+6∫xdx+6∫dx   b. −2∫x2dx+6∫xdx+6∫dx…

A:

Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where 0 < |z| < T.

A: Cauchy residue theorem is one of the method to evaluate the integral of analytic functions.…

Q: Evaluate the iterated integral. 6. 7 8 (x² + y² + z² ) dx dy dz -6 0 0 6 7 8 (x² + y² + z² )dx dy dz…

A:

Q: 3. Show that а" (1 — 2)" dа а" (1 — 2)"da, where m, n are positive integers. (Use integration by…

A: To prove that ∫01xn1-xmdx=∫01xm1-xndx Where m,n are positive integers.

Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…