Which of the following is the result of applying the substitution u = 4x – 9 to the integral (4х — 9)20 dx? 20 du u 1 (b) u20 du (a) 1 (d) 4 23 20 23 (c) 4 u4º du -1

Q: dx Evaluate the integral V1 + 9x² 1) Which substitution will change the integral into one of the…

A:

Q: 2x Evaluate the improper integral J da, if it exists. (z² + 121)?

A: Use the substitution method of integration

Q: 11. Evaluate the following integrals: (a) 2+ 2- dt 1/2 (b) ["a 1 dt 2. (c) I12-x| dx

A:

Q: d.x (a) Evaluate the integral In(8x) using the substitution u = ln(8x). d.x +C T In(82)

A:

Q: Evaluate the following integral. JJ (xy + xz + yz) dV; D = {(x,y.z): - 25xs2, - 4sys4, -1szs1} JJI…

A: ∬∫Bf(x,y,z) dV = ∫rs∫cd∫ab f(x,y,z) dx dy dz                         where , B=a,b×c,d×r,s

Q: 3. Compute the following integrals : a) cos e1+3sine de b) S xdx Va+x4

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

Q: Which of the following integrals is equal to (3x-5) dr if u=3x-7? (A (u+2) du 8/3 -2 -1 / (u-2) du…

A:

Q: Consider the indefinite integral r523 + 2х? — 72х-32 2x2 – 72x dx 16 - Then the integrand decomposes…

A: Evaluate definite integral ∫5x3+2x2-72x-32x2-16dx

Q: Which of the following integrals will yield In u+ C? A. SE B. S- x+1 D. S dx xdx C. S 2rdx = x+1 O…

A: From the following integrals will yield ln u+C Note:     Multiple questions are given, we are answer…

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

A:

Q: 8x Evaluate the given integral Jo (4+x²)2 dx using the substitution u = 4 + x². A. Estimate to three…

A: topic - definite integration

Q: Which of the following integrals is equal to ( 3x – 5) dx if u=3x – 7? (A (u) du / (u+2) du B © :/…

A: We know by properties of definite integrals, if a-b=(p-q)/m then, ∫baf(x)dx= 1/m * ∫qpf(x)dx

Q: Evaluate |- e*dz where c is |z|=3 using Cauchy's integral formula „(1+2),

A:

Q: Evaluate the integral 24 11) dx, by making the appropriate substitution: u = Ja* (2* – 11)*“dz =

A: ∫ un du =un+1n+1+C

Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector:…

Q: For 1/2 U -dx and using the substitution -du -du 4u √4-(2u²) ² 4u du -du 1/2, the resulting integral…

A: In this question, we want to know the Integral form after substitution.

Q: 2x Evaluate the improper integral J dx, if it exists. (12 + 81)2 -00

A:

Q: 2. Evaluate the integral using FTC Part 2. d e²-t st². t dt dx

A:

Q: 3T en: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (").

A: Given query is to find the indicated function.

Q: Consider the indefinite integral + 222 – 29z – 21 da. 1² – 9 The integrand decomposes into the form…

A: Let's find.

Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: In evaluating z(4– æ)šdx,if we use the substitution that u = 4 – x, then what will be the resulting…

A: Given that, The integral is following, I=∫x(4-x)13dx If we substitute,   u = 4 - x, the what will be…

Q: 4 ∞ dy dx J I+ 4? 2. 00

A: To find the integration

Q: Evaluate the integral. et i + 3t2 j + In(5t) k) dt + C

A: We have to evaluate the given integrate…

Q: The evaluation of the integral - de is +In 3 (C) 0 cos3e (i) 4 (ii) + In 3 3. (iii) None of these…

A:

Q: Apply Green's Theoren to evaluate the integral. C6x+y) dx + (3xy"+4y) dy ter

A: Given integration is ∮c(6x+y3)dx+(3xy2+4y)dy C : Any simple curve in the plane for which Green's…

Q: Evaluate the improper integral: 17 dx a) O-17 b) Odiverges c) 17 d) O34 e) OV17 8 8.

A: Given integral is ∫-∞∞17x2dx. Adjust integral based on undefined points. There is undefined points…

Q: For O S O 1/2 dx and using the substitution 1/2, the resulting integral takes the form: U=X U du -du…

A:

Q: The result of the following double integral is 2 SS T oxy²z dxdzdy = ? -2°0 None of he others O -21…

A:

Q: Evaluate the integral 35 dz 4 by making the substitution u = x* – 6. +C

A: integration

Q: 15. Evaluate the following integrals: (b) , Tax+1)3/2 (c) f, (8)05xdx. 30 8 dx (a) J 7x+5)1/3 ' -dx,

A:

Q: 3z+4 dr Use the appropriate substitution to evaluate the following integrals: e %3D O e3a+4 + C ©…

A:

Q: 14 10ху To compute / Js x²+y²+3 ) axa you do the u substitution: u = (Notice that this is a…

A: Solution is here

Q: In evaluating z(4– 2)šdx,if we use the substitution that u = 4– 2, then what will be the resulting…

A:

Q: 2. Evaluate the integral 8- (a) L« (4t5/2 – 3t3/2) dt (d) 2 - Vt dt r4 (e) t2 cos e de JT/4

A: The objective is to find the values of given integrals

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

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

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 a. dz S dz b. So 22(2-1)" z(z-2)4…

A:

Q: 1. Use substitution to evaluate the following integrals: dt arctan(2t) dt (b) t/1– In't (а) 1+ 4t2

A:

Q: Evaluate the double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

A:

Q: 2_ Calculate the generalized integral. x In r dx J. (1+12)3

A: The given integral: Calculate the above integral:

Q: Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let…

A:

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: The result of the following double integral is 2 2 у ST (6 x² y - 5 e)dxdy= ? 0. -2 y 909 -20e? +…

A:

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: Evaluate the following integral from a=-0.4 to b=7.6 with single application of Simpson's 1/3 rule b…

A: The solution is given as

Q: find the integral from 1 to 4 of (3t^(3/2) i+(t+4)(√t)k)dt

A: The given expression is ∫143t32i+t+4tkdt. Evaluate the value of integral. Here we use the formula…

Q: 1. Evaluate the integral using the given substitution xcos(9x2)dx u = 9x2

A:

Q: Evaluate the integral in (7x) -dx. Choose the correct answer below. O A. - In (x) - 16 1 +C 16x* -In…

A:

Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 7/3 "s(:) dz 3 -2 2p (2)f…

A:

Q: Consider the indefinite integral (5x³ + 4x? 73x – 52 dx 16 Then the integrand decomposes into the…

A: