EVC the ction: 1 dx x2/3 (1+x!/3)

Q: nction 'a' is 1+eaz at its pole

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Q: Evaluate in terms of beta function: (1 – +) dx. - O-8(금, 금) O-8(를, 승) O B)

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Q: 19x + 87x2 -) dx (Use Term by term integration) O (38x + 58) Væ + C O (38 + 58 /æ)V¤ + C O (38 +…

A: Given :                      ∫19x + 87x2xxdx

Q: Using Boole's Rule, Evaluate (x² + 3y²)dxdy

A: Given:                ∫02∫0yx2+3y2dxdy To do: Evaluate the integral using Boole's rule.

Q: Arcsin(x/y) = 4x + 3y %3D

A: Function given is- Arcsinxy=4x+3y We need to determine the second derivative (y'') or d2ydx2 for the…

Q: | cosh(In z) dr

A: Given:  Let I=∫1e coshln x dx To Find: To evaluate the given integral.

Q: Evaluate integration 1/(x^2-9)^(3/2) dx using trigonometry substitution

A: Consider the given integral as ∫1x2-932dx. We use the trigonometric substitution x=3sect to evaluate…

Q: integsate Sin ue go. 1og (Casu) where n-782

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Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

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Q: dx Evaluate x²/4 x²

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Q: xsin x -dx, a > 0. x +a 15. Evaluate by method of residues |

A: Residue theorem

Q: ((2- sec?x) emaie sec³x sec( 3A – x) In (ale) What should be the value of A for -dx to be integrable…

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Q: 3cos3x - 1 To evaluate dx, the integrand can be transformed to 1- sin?x

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Q: ) Isinx-sinyls lx-y!

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Q: sec x2-1 1

A: Given problem:-

Q: |x Arcsec 3x dx = uv- -Svau Using Integration By Parts, Find UV- du x2 Arcsec 3x dx x²-1 = x2 Arcsec…

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Q: f(x)=\arctan (1-x),[0,1]

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Q: | sin“ x cos' x dx 4. Integrate:

A: Given: ∫sin14x cos5x dx  To find: Value of the integral.

Q: Evaluate the definite integral. "1/3 3 dx V1- 9x²

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Q: arctan(x) dx = x arctan(x) - 2 In(1+ x?) + c

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Q: u) sec(2-x)tan(2-x)dx

A: To evaluate ∫sec2-xtan2-xdx

Q: 2. Using trigonometric substitution, what is f- vx²-9 dx ?

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Q: YOUR TURN 6 Find xV3 + x dx form Sub In be 1. 2.

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Q: ‚arcsin(1+x²)] y'of y = In cscya

A: Given y=lnearcsin1+x2cscxWe need to find y'

Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

Q: 10. S(tan x – 1)²dx

A: Topic:- application of integration

Q: Luse integnal a stande substutuon to educe the 3(3x+12) dx,u= 3X +12 du 3,2 * du= 3,2dx

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Q: sin(5x) dx 2+сos(5x) اخترأحد الخيارات х + tan(5x) + с.ао —In | 2 + сos(5ӕ) | +с.Ь 1 +c.c 2+сos(5ӕ)…

A: Since , in the given integration problem we have derivative of denominator in numerator so we will…

Q: sin(3x) %3D y(x) = 4+5cos(2x)

A: we have to derivative

Q: Che number ofunits in Z31[x] is

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Q: antiderivate of y = sin x + 6x2

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Q: 3cos3x (3cos³x - 1 1- sin?x To evaluate dx, the integrand can be transformed to

A: Given: - The integral is, ∫3cos3x-11-sin2xdx To find: - The given integrate can be transformed to.…

Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

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Q: sinh-1x = In (x + vx² + 1) %3D

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Q: ´In²sinx In the expression dx , the integrand is tanx

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Q: 1 Evaluate – -dx 1+ 3sin"x + 8cos™x

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Q: ·sec-x)" sec'x 23. What should be the value of A for -dx to be integrable using the formula | u" du?…

A: the integration of the integral is (2-sec2x) eln(pi/e)sec3x/Sec(3A-x).

Q: Scoth (2) dx

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Q: i) Integrate  f sin 3x dx                                                                       ii)…

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Q: double integral ſp x³ydA

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Q: 0sin 2 x coOS x dx

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Q: O IT 3 tan'z sec z dx

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Q: 9. 1 dx - 3

A: Solution

Q: 3 dx 23.

A: Given:

Q: За + 2 dx. V6 – x2 x2 + c Evaluate the integral - а) 2 arcsin( 6а) — 3у6 — 2? +с - b) 2 агcsin( ба)…

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Q: separable 9-X(2lnX+1) Sin y+ ycosy

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Q: dx (5-4x-x²) 18. 8. f

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Q: Use integration by substitution or integration by parts as appropriate to evaluate Axsin (Bx) dx…

A: We are given A=3 and B=3 now putting the values in integral it becomes ∫0π23xsin(3x) dx first we…

Q: 3x+2 b. Evaluate dx, using a suitable technique and provide the reason for -2 (3x²+4x+2)* your…

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Q: ,2x cos 3x dx

A: We need to integrate given function.