Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 + 12y – 36y2 dy 3 sin -1 (1+ 6y – 36y²) 36,2) 2 + бу— 1 7 1 2 + -1/ бу — 1 + C x - 12 V 36 (y-) 108

Q: Evaluate the integrals in Exercises using integration by parts. 2. |0 cos m0 do 4. f* sin xde * cos…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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Q: In approximation of fx)dx by Romberg Integration, if R,=0.25 and R21 =0.2525, then R22 o None of…

A: The objective is to find the value of R22. It is provided that in approximation of ∫abfxdx by…

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Q: If 9. 10 f(2)dæ = /: | F(2)dx - / f(x)dæ, f(x)dx + %3| 3 9, what are the bounds of integration for…

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Q: Evaluate the integral r4 pr=/2)+1 2x –- y -dx dy 2 o Jx=y/2 from Example 1 directly by integration…

A: Given,         ∫04∫x=y2x=y2+12x-y2dxdy=?

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A: Here, we need to sketch the domains of integration.

Q: Q.4 Show that in the following problems, the line integrals are independent of path of integration…

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

A: We have to match the correct representation of u to evaluate the given integrals by the method of…

Q: Consider V /3x² + 3y²dxdy The integral cannot be solved analytically using basic integration…

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Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

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: 1. Evaluate the given double integral by first changing its order of integration 1 •1-y² ye(1-x)² dx…

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Q: 2. Evaluate the integrals. (a) S (b) [9rc (c) J (d) O 1+ e²r 9x cot(x²)dx -do -dx cos sin² 0 +1 -dx…

A: As per the guidelines we can solve 3 parts only

Q: I.Evaluate the ff. iterated integrals. • 7d/2 ptan y sec y 1. .3 cos' ydxdy JJ

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

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

A: Let's find.

Q: We'll now apply the integration by parts procedure to the new integral e70 cos(80) d0, letting U =…

A: The given integral,∫e7θ cos(8θ) dθ

Q: Evaluate the iterated integral. 7 8 6 | // * +v° + 2²) dx dy dz -6 0 0 / /(x² + x² + z²)dx dy dz i…

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Q: Reduce to first order and solve. (1 - x2 )y" - 2xy' + 2y = 0, y1 = x. Use : fp dx = In [1/(1- x²)] ,…

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Q: Compute the following integrals. 1 t3 (a) dt. Jo V4+ t² (b) e6x cos (3e2) dx. (Hint: you might need…

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Q: Q#5 Evaluate the integrals using the indicated substitution. i) S 2x(x² + 1)23dx; u = x² + 1 %3D ii)…

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

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

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Q: Find the value of the line integral 6xy dx + (3x² + 4y2)dy, where C is an ellipse 16 + = 1 from (4,…

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

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Q: Q.2. Calculate the integral of: f(x) = (3x+1) from a=-0.2 to b=0.6 by using Simpson's Rules only and…

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Q: To find the definite integral Vx2 + 64 dx, apply the basic integration rule. Let u = x2 + 64.…

A: We have to find the definite integral. Here we are using integration by substitution.

Q: 14 Find the integrals using integration by parts. -2 b. JVF In Vxdx a.

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Q: Find the complete integral of 1 dz 1 dz 1 dz z dxz Ixe z z dx2 = x1 X2 X3.

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Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: Set up an iterated triple integral equal to √3-x² | = • S√³/3 SO √√3 x² + y² 3 2-₁/4-x²-y² 2y dz dy…

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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: 39. Use a software application to compute the integrals у — х dx dy (x + y)³ у — х dy dx Jo (x + y)³…

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

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Q: The value of the improper integral / 36 z² e ² dz = 12e1 O - 36e 1 O 36e 1 O 12e 1

A: We need to evaluate the value of the following integral I = ∫1∞36x2e-x3dx

Q: 3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1…

A: Integral by parts

Q: Supply the missing integrand and the limits of integration ... CT/2 c2sin e r cos²0 dr de de •x/2…

A: Question- Supply the missing integrand and limit of integration.

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

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Q: 1+1 dz is 1+ z6 By comparison test, the improper integral

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Q: 25. Describe the domain of integration of the following integral: LLE /5-x2=22 f(x, y, z) dy dx dz…

A: Domain can be discovered using the bounds of the integral. Domain is 1≤y≤5-x2-z2.

Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

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Q: 1 dy 3 yz-+ y7 = 1, when x = 0, y = 3 dx

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Q: If the order of integration is reversed for the double integral Sa ez+yYdydx, the integral will…

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 +…

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Q: Consider the indefinite integral " (5x³ + 4x² – 75x – 68 22 – 16 da Then the integrand decomposes…

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Q: Find the value of the line integral SaF· dr. HintL If F is conservative, the integration may be…

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Q: Find the double integral ff (x² + y² do, over R={(x, y):-1≤ x ≤ 1,0 ≤ y ≤ 2}. 1.

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

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: 2. Use Romberg integration to compute R3.3 for the following integrals. 0.75 (cos x) dx a. x In(x +…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…