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

Q: In the function given. Evaluate the integrals.

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Q: What is the general solution of dx? (1 — 2е3») + C 6 (1 — 2е3г) 1 + C 6 (1 — 2е3г) - 1 + C 18(1 –…

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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: Evaluate xe-X dx, if it exists. O 1) 1/2 2) 1 3) 1-e 4) It does not exist.

A: We have to evaluate given integral

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

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Q: Bernoulli Equation (11) (x²y* – 1)ax + x³y³dy = 0 (12) x2 + 2xy dx

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Q: Find the general solution of dy/dx= xy-y/x^2-5x+

A: To find the general solution of the below differential equation. dydx=xy−yx2−5x+6

Q: 3. (1+3e )dx+3e"1- dy =0 Ans. x + 3y e = C

A: Given,1+3exydx+3exy1-xydy=0

Q: x²+x-2 J (x2–1)(2x-x²) dx can be resolved into dx dx. + DS x-2 dx dx.. A x- х-2 dx x+1 x+2 - dx do.…

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Q: 17. (бх - 2у + ye")dx + (хе" - 2x)dy 3D0 19. (у? + ysenx)dx +(у+2хy- сos x)dy 3D 0 21. (2x-e' + ye*…

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Q: What does f(z) dz mean?

A: Given that: ∫f(x)dx

Q: 5 6 7 | || ? +y² +²) dx dy e -5 0 0

A: Given: ∫-55∫06∫07x2+y2+z2dxdydz

Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x −…

A: Given: x2-1+2ydx + 1-x2dy = 0 , when x=2, y=1. Solve the given differential equation. Concept used:…

Q: 2 -2 [ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy. We have Select one: True False

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Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

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Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

A: Given ∫x2x2+34dx

Q: 12 d3x(t) 5 dt3 d²x(t) dt2 + 5x(t) = 3cos(2t) d²x(0) = 2, dx(0) 1, x(0) = 1 dt2 dt

A: Given differential equation is

Q: 4) (x- y)dx+(3x+ y)dy =0, when x = 2, y = -1 5) (3x - 2 y²) y'= 2.xy, when x = 0, y =-1

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Q: ( 2x – 3y + 1)dx – (3x + 5y – 6)dy = 0 %3D O 2x² – 5y² = 6xy – 2x + 12y = C O 2x² - 5y² - 6xy – 2x +…

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Q: 6. J 4 x4-1 -dx

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Q: /2-x2 Evaluate *Ty dy dx x²+y² Select one: a. Non of them b. 1 2 - V2 С. 1 1 V2 d. 1 3

A: We will find out the required value of given integral.

Q: 12] (1+e* 1-ex S dx 3x2+14x+13 (3] S 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: 17. If y = x, then dy/dx (a) x²-² (b) x²-1 lnx (c) x²²(1-In² x) (d) x²-²(1–In x) (e) None of these

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Q: 2) (Зx2у + 4eУ)dx + (x3 + 4хеУ + 2у)dy

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Q: -2x2 + 7x 8 | dx J (a + 2)(2x – 1)(1 – 2) (A) -4 ln |x + 2|+ ln |2x – 1| + In |1 – x| + C (B) 2 ln…

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Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

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

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Q: 1 c2(1-z) Evaluate Sa-2) s(1-;-2) dy dx dz

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Q: dæ4 evaluated at x = -1 dx evaluated at x = –1 dx? evaluated at x = -1 dx3 dªx4 evaluated at x = -1…

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Q: ( 2x – 3y + 1)dx – (3x + 5y – 6)dy = 0 %3D O 2x² – 5y² = 6xy = 2x + 12y = C O 2x² - 5y² - 6xy – 2x +…

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Q: 2r –1 15. Evaluate dx. (x– 2)(x+1)' A) hx- 2| + hịx + 1| +C C) -hx – 2| + Inx + 1|+C B) hx- 2| – hịx…

A: To evaluate: ∫2x-1(x-2)(x+1)dx

Q: (2x+1) 5. S (x+2)*(z–1)ª -dx

A: The given integral,∫(2x+1)x+24x-14dx

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: ^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: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1) b. (x + 1) y = (x −…

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Q: 3. Evaluate: e-x²+2x dx (Hint: let t = (x – 1)²) |

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Q: ∫1/x2√4+1/x dx, u=4+1

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Q: I’m sorry, I meant #4

A: Let x= 3 sin uSo, dx= 3 cos u du

Q: (x² + 2xy − 4y²) dx − (x² − 8xy − 4y²) dy = 0

A: First, divide the equation (x² + 2xy − 4y²) dx − (x² − 8xy − 4y²) dy = 0 by dx. (x² + 2xy − 4y²) dx…

Q: x2-7 2. S dx х3-12х+16 9y+14 3. S (y-2)(y²+4) ay 4. S х3-х2+1 dx (x2+2х+2)2

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Q: e2x dx= 1+ex A ex – In(1+ e*) + C B e2x + In(1 + e*) + C © 2e2x – In(1+ e*) +C D e2х- in(1 + e*) + с

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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: True or False: If / X (x − 1)(x + 2) dx then B = dx = 1 -In(x - 1) + Bln(x + 2) + C 3

A: Consider the integral, ∫xx-1x+2dx=13lnx-1+Blnx+2+C then B=13. To determine whether it is true or…

Q: d²y dy -2 +4y dx 2e 2x dx2 x3 an is given hy:

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Q: - S (x+1)dx в с х-1 (х-1)?, A If (x+2)(x– 1)² dx , the values of A & C respectively are + %3! x+2

A: The given equation is as follows. Solve the function by partial fractions as follows.