3 Question 1 Evaluate dx. x2 + 4 3 Question 2 Evaluate dr. x² – 4 x + 1 dr. x³ – 2x2 + x Question 3 Evaluate

Q: 1) x(x + 1) dx S (3) x² x² +9 dx (2) √ x(x x(x + 1)³ dx (4) (x² + 1) cos x dx

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: + 1 =2e- dy

A: Given, Can be rewritten as

Q: (3 - x) dx is equal to ° S (3 − x) dx + ["' (3 + x) dx °₁ (3 - x) dx ° L₁ (3+2)dz + f (3-2) x) dx x)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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: 7 I √49-x² 49-x²-z² Ľ -V 49-x² 1 √49−x²−z² (x² + y² + z²)¹/2 dy dz dx =

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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: 1 Ax dx = fe 2. 1 A. e* +1 4 1 1 -4 + e 4 В. 4 1 С. е 4 4 1 D. 1 e -- 4 4 1 e*+1 4 -4 Е. -

A: Formula: ∫eaxdx=eaxa

Q: 2-x 4x + 4x - -m(4x* + 4x – 3) + In| (2x 2x- – 3 x +1 x(x + 3)(x + 2)(x – 1) 1 (x + 3)*(x – 1)ª I…

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Q: 0.1 0.2 dz dy dx 3-3 X-る りー-oハ そ--0,2

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Q: 1. S (5x-12) dx 2. S x³-6x² +8x 3. S -(3 cos² 0 +8 cose-12) sine de cos³ 0+7cos² 0+ 12 cos 0 dx…

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Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: ) ور شم( موم 2 4-x 2 2 4-x 2 x++y¯+z° e - dz dy dx -2

A: To evaluate the below integral. ∫−22∫04−x2∫04−x2−y2e−x2+y2+z23/2dz dy dx

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

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Q: 4. (9% +3³ +2²) dx 5. J 10% dx (10% +1) 6. f2x(ex+1-2²) dx

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Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: 15. /7.- dt 16. x+ 3 dx P + f - 21 2r - &r

A: Solution:Given      ∫dtt3+t2-2tFormula:∫dxx=log x+C

Q: (2.x+ 5y)dx + (4.x – 5y)dy =

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Q: 3. Differentiate y = 2x-1 - with respect to x and then evaluate 2 x(x – 1) -dx (2x – 1)2

A: Given and

Q: 1. ſx² e*³ Sx² e**dx 2. cos'xsinxdx sin3xsin 2x dx 3.

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Q: Evaluate the definite integral using the given values

A: Given: ∫26x3dx=320, ∫26x dx=16, ∫26dx=4 We have to evaluate ∫266x-18x3dx Solution:…

Q: (3) (2x – 3y – 2)dx + (6(2x – 3y) – 2)dy = 0. - - %3D

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Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: 6. J 4 x4-1 -dx

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Q: 3) (3x- 2y+1)dx+(3x– 2y+3)dy = 0

A: We have to find

Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: 2. S 8sin*x dx 3. S 8cos*x dx

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Q: 8. · √(x) √₁² 1 9. J 5x + 1 dx 10. S 3x +9 (x) √√x² - 1 dx dx

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Q: :) 3 1 19. + dx x3 3x 20. | (2.x2 + x – 1)dx 2y4 + 1 / 2y4 Зуз 21. ip- 1 1 22. / (VE+1- + sin x – e"…

A: 19.  Let the given be I  I = ∫3x3 - 2x3 + 13xdx Now integrating given integral , we get  ⇒I = ∫3x-13…

Q: (2,5, – 6) | 16x dx + 4y dy + 2z dz (0,0,0)

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Q: 7. [(4cosx+3sin.x)*dx 8. ſcos°(3y)dy 1 (у-5)3 v – 5)³ 9. -dy 7 y3 (3 – 2 cscx)² 10. cotx

A: Integrate above function.

Q: 1. S(x +5)5 dx 2. S(9+ x)² dx 3. S(2x +5)3 dx 4. S(3x + 5)²dx 5. S 2x V1 +x² dx 6. Sex+3 dx 7. S5e3x…

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Q: (4) (2xcosy+3x²y)dx+(x³ – x²siny-3)dy=0

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Q: 3 [[ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy 4y³ We have Select one: True False

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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: 3x Question 4 Evaluate dx. 4 + e6x 3 Question 5 Evaluate dx. V4 – x2 | 3x Question 6 Evaluate dx. V4…

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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: 7. (у — 2) dx + (3x — у) dy — 0. ANS. 12x = 3y + 2 + c(y – 2)-3. -

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Q: x² 1 arctan 16 2(x – 3) + 3 -dx = J (2x² – 6x + 13)² + c 2 x² – 6x + 13

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Q: ∫1/x2√4+1/x dx, u=4+1

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Q: (3x² + 8x – 12)dx - x3 + 7x² + 12x x² – 12x + 4 dx (x2 — Зх + 2)2 t² + 4t + 10 dt t3 + 2t² + 5t dy 3…

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: Зх-1 dx; J x²+10x+28 Зх— 1 Sa :dx (x + 5)² + 25' Зх — 1 -dx Ja+ 1)² + 1 Option 3 Option 1 Зх - 1 dx…

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Q: (8 cos x cos y + 4 sin x sin 2y + 1) dx – 8(sin x sin y + cos x cos 2 2y) dy = 0

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Q: G. q 1-Jx 휴-1 14 314 (x+1) dx 1114 X2 (x-1) X2(x-1) = Anㅎ Sa ㅋ. S? 1+Sx dx=4n 은

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PER…

Q: 3.2 = (9x + 4y + 1)} dx 3 Let u = 9x+4y+1

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Q: 1/2 (1) 1 x-1/2 dr. 2 + 1 -1 (2) e In x dx In x

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Q: Find the General Solution 1. 2(2xy + 4y -3)dx + (x+2)2dy=0

A: 1) 2(2xy + 4y -3)dx + (x+2)2dy=0 Repost the next parts.

Q: 1. Integration by parts: 2 3 .5x X°e dx

A:

Q: 4. (6xy³ + 2y*)dx + (9x?y² + 8xy³)dy = 0 5. (у2 — 2ху + 6х) dх — (x? — 2ху + 2) dy — 0 When: x =…

A:

Q: 1. S Vx²-1 dx dx 4. S x² /x2-9 dx 5. J 16-9x 2. S dx x/16-9x2 4-x2 3. J 1+x2 dx

A: Given