2x – 1 - -dx x2 – 6x + 18 6x + 18 (구) -ㅇ 2 In Va? – 6x + 18 + 2 In +arctan 3 3 3 O A O B

Q: (2x + 4) + 1 dx- x² + 4x + 5 x² + 2x– 10 2 (2x + 4) + 1 2 Consider dx = x2 (x² + 4x + 5) dx.…

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Q: 5. Evaluate: (а) ( 5х* -х-4) dx (b) f( 2x +4)(3x + 6)dx

A: 5. (a) We will evaluate the integral ∫5x2-x-4dx

Q: 3 wu= 2-x. [ w/2-xdx= If U = | x/2-x dx= 3 (2 – u)Jūdu Luūdu -1 .3 uſudu D (2 – u)Vūdu -1

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Q: 9. Integral (2x-5) dx x²5x+3

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Q: O)³ = /1+ (y')² = /1+ (y')* = 3 + d²y dx2 a3y 3? +1 ax3 at

A: Note:  according to our guidelines we can answer only first three subparts To determine the order…

Q: 3. II Azy'dz dy = 2y°(3² – 1)dy | 2y (y? – 1)dy 1

A: Given that a double integration .We use general  property of integration to solve this integration.…

Q: –2x x- -dx x2+e-2r A (x-e-2r) x²+e-2x xp- B -2 (х—е -2) x²+e-2x xp- e -2r dx x²+e-2r x²+e -2x D E)…

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Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: (1) ਤ + x2 x2 + 3 dx (2) In 2 -e ex 1+e dx x +7 (3) --x-6 dx

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Q: f(x)dx = 2, 5 and 8 f(x)dx = -5, then, 8 f(x)dx = -3

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Q: 1.S (3x5 – 2x – 5x – 3) dx 2.5 (y? – 1) (3+2y) dy 3.S V + 5VX³ dx

A: Dear student. Since you have posted many sub-parts, in our policy, i have answering the first…

Q: III. Evaluate 4 - x -dx. V16 – x2

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Q: .3 y = 2x + 5x from the point (-2,-26) to the point (4,148), you'd have to compute | f(x)dx

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Q: 3 + 2/5x-3 dx. Find 4x+1 - Vez

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Q: 7.5- yy - 9 4+9) dy -6- 8.S 1 dx e2x+ e-2x

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Q: x² - 2x x3 3x² - - dx -In 1x³ 3x² 1 + C Option 1 Option 3 - -In 1x³ 3x² 1 + C In 1x³ 3x²1+ C Option…

A: SOLUTION-

Q: 5. Evaluate. |2x – 4| dx -

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Q: -2x +5 Evaluate 10-4x -2y dy dx 3x 25 3

A: The given integral is: ∫01∫3x-2x+5(10-4x-2y)dy dx

Q: 7. Evaluate x²+2 + (x − 1)(x − 4)(x+2) - -dx.

A: ∫1ax+b dx =1alnax+b+C.

Q: 3 4 (5х + 3у) dx dy 4 (5х + Зу) dx dy %3

A: Evaluate the iterated integral∫03∫045x+3ydx dy

Q: 4 sec*(x) rind tha ualı Find the value of ((x* - 5x² – 6x)“ 4x³ - 10x – 6 dx. (x4–5x²–6x)* - a) 4…

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Q: 2 1. x(-x² + 1) dx 16 dx 4x2 2. 3. dx x3/7 -V4x dx 4. 5. . (-2x! – x295) dx

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

Q: x7= - 3x + 18 JZ - 54 in (3+ 57) + c 3/2 2 dx = %3D 3 + VX 3

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Q: ex-4e-x ex 2 x-² / + C ex Option 1 dx 2 x + ² + C ex O Option 3 x+2 ex + C O Option 2 x-2e * +C O…

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Q: dy If y = ( a² +1) (x³ + 3) dx %3D O 5x^4 + 3x^2+ 6x 6x^3 O 2x + 3x^2 O 2x^2 +2x+ 3x^5+9x^2…

A: Question 1,Given,            y=x2+1x3+3To find: dydx

Q: 22 Evaluate S- dx. 3/2 +1

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Q: 5. Show that (x² + 1)e-* dx = -x²e-x – 2xe-x – 3e-x +C

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Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: Which of the following is correct? * 3 3 (3 In(x²)) = dx (3 In(x²)) = dx Option 1 O Option 2 d 6 (3…

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Q: 46) Evaluate V(3r + 1)dx 2(3r+1)7 O s(3z+1) 2 O 2(3z+1)7 +c 3 O D(3r+1)1 + c 2

A: We have to solve the given integration

Q: Evaluate ( ax"+5ax*+12ax*+llax²+3ax+10a x4+5z³+14x²+17x+7 dx * + 24. + In |a2 + 3x + 7| - arctan In…

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Q: 5) Evaluate x2n-1e-kx² dx

A: Gamma Function: Γ(n)=∫0∞tn-1 e-t dt And Γ(n)=(n-1)!

Q: - 2r³+ 4x²+ 3 -dx is equivalent to x²(x²+ 1) 2x- + - 1 dx x?+1) 2x –1 dx x²+2, 3 B © /: 2x – 1 x+1…

A: Given problem:-

Q: 14-2x 1. ! ] dydx 0 2 2. dxdy 0 y 11-r 3. dycx o 1-x 4. [[ dydx 0 0

A: Answer 1: changing dy dx to dx dy; limits of integration: 0 ≤ x ≤  [2 - (y/2)] 2 ≤ y ≤ 4

Q: Evaluate the definite integral using the given values

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Q: x2 -dx 1+ x4 -dx (x² + 1)²(x² + 2.x + 2) 1 -dt, for a> |6|. > [b]. а a +bsent

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Q: 1. Evaluate [(2sin 2x+3Tanx – 5 e-5* +4x' -7) dx .

A: Integrate each term

Q: ^4-x² •6-z 2. Evaluate: dy dz dx. 3x2 4-z 3. Evaluate: dx dy dz. Jo Jo 0.

A: To solve the given triple integrals

Q: 1 dx oraz 1 dx. 1+ x² Oblicz 1+ x²

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Q: | 3tan-1(x)dx = %3D 2프-21n2 In(4) 2/3 None 을 + m2 2 In(÷) | 3 3 - In(4) 6 3

A: Solve by parts method of integration.

Q: 6. Jo ex-3 S dx = 1- e2 – 9 2- e+3 2- e2+3 4- e+2

A: 6. We need to evaluate the following definite integral ∫01e2x-9ex-3dx

Q: 3. dx Vx (2+3/2)5 3 3 dx = Vx (2+3,/x)5 Vx (2+3x)5 X,

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Q: L() tu(t-3) e6-3s ( 1 + (s+2} 3 s+2 e2-3« ( + ) o 1 (s+2} S+2 e-3+ ( +) o 1 (s+2} s+2 ( e-6-3s 1 3 +…

A: We will find out the required value.

Q: integrate (2x + sqrt(x)) dx from 3 to - 6 A. 27 +2√3+4√6 B. 27 + 2√3 C. 27 - 2√3+ 4√6 D. 27-4√6

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Q: 8. (b)/2 -- xe dx

A: Integration using byparts: where u is the first function and dv is the second chosen using…

Q: 3. (a) Determine 3 4 dx VI - x², + x2 (b) Determine 3 + V1- x2 4 dx 1+ x2

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Q: 19-x 2 Find -dx 2 x² 5.

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Q: 1/2 Scave [ (a²-x² - x²) ¹²h dx (8) = √5 (9² - x²)³/²2 [³ (a²-x²) ¹1²2 0/² ] + c 15

A: Given:       ∫a2x6-x8dx Rewrite:      =∫x3a2-x2dx substitute u=a2-x2→dudx=-2x→dx=-12xdu…

Q: (4 - x2)3/2 dx 3

A: Consider, I=423∫-22(4-x2)3/2dx I =4232∫02(4-x2)3/2 dx   since f(x) is even function that is…