10. f (Se e-3x XE -3e*-4e*)dx 4e)dx e-2

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

Q: 16 (1.) 2XInX 2 dy/dx (2. if 4 = cosh 2 JX +1 %3D 213 dx (3.) 4+x2

A: Question 1 is solved by substitution method. Solving other questions are against the policy of…

Q: Solve dy 2 dx - dy + 2y = 7 cos x + 5et dx -3-

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Q: 5. 6. Sexcos2x dx |— S- dx 3 (x + 2)² − (x+2) ² -

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Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: Compute dy / dx and d2y / dx2              x 2 - 4y 2 = 8

A: The differentiation is a process of finding the rate of change of one variable with respect to…

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: 5-(1+x')(dy-dx)= 2.xydx;

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Q: 2 4 Evaluate Sx dz dy dx 3

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Q: Evaluate the integrals

A: Given I=∫01∫03-3x∫03-3x-y1dzdydx

Q: 9. Integrate: Ja (x- 1) cos(x? - 2x) dx

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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

Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

Q: 4. 5. (3t dt)/((t² + 3)) dx/ (3x + 1)

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: (a) (Ex) ((Ax --> Bd) --> Ky) (b) (Ex) ~ (Dx v Cy) (c) -(x) (Dy --> (Hx v ~Ga))

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Q: Evaluate the integrals

A: The given integration is: ∫03∫09-x2∫09-x2 dz dy dx Here first to solve the inside integration with…

Q: 25. (ye*" – 2y³) dx + (x e*' – 6xy² – 2y) dy = 0; when x = 0, y = 2. ANS. e* = 2xy³ + y² – 3.

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Q: 2 Find So (3x2 + 4y³) dy dx.

A: Topic:- double integration

Q: (A) Evaluate / (4x – 5) (4/x + 4x) dx. x² + 3x - 6 (B) Find dy -, if y = 3 -)4 when x = 1 %3D dx

A: *we have to perform integration operation in A & differentiation operation in B.

Q: 1. (2x – 3y) dx + (2y – 3x) dy = 0 - -

A: According to our guidelines we can answer only three subparts of a question, or first question and…

Q: X = e not inelude th degreo QUmbelin

A: The triangle is shown in diagram ,

Q: 1. S 2x (x² + 1)5 dx 2, | 3х 4) ° . 3. sec2(4x) dx e8x dx 4.

A: We can use integration by substitution when a function and its derivatives are presented in the same…

Q: 4. If Kx)dx = k, ] fx)dx = (x-f(x) )dx what is the value of Ax)dx? Use: [Ax) - g(x) ]dx =[ fx)dx-J…

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Q: Find d^2y/dx^2 at (-1,-2) if 3x^3-2x^2+x = y^3+2y^2 +3y.

A: Given function is: 3x3-2x2+x=y3+2y2+3y Let us consider: y'=dydx ; y''=d2ydx2 Differentiating both…

Q: Find dy/dx at the point (2,-2) if 3y2-4x2+4=0.

A: Find dy/dx at the point (2,-2) if 3y2-4x2+4=0.

Q: 2 Evaluate S S dx dy dz.

A: Evaluating the definite integral

Q: -16 dx 1. X=2 sec(e) 2. x= 2sin(e) 4-X dx 3. X= 4tan(e) 4. X= 4sec(e) SV16+ x² dx x²-4 dx

A: See the details solution in below

Q: Solve for dy/dx. y=((5x-3)/(4-3x))^-3

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Q: dy If y = 10**-1, solve for dx dy = 2x(ln 10)10*²-1 dy = (In 10)10*²-1 dx dx Option 4 Option 1 dy =…

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Q: find dy/dx of x^5y-xy^5=1

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Q: 4- S" e-x* dx 5- Vy e-y² dy

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Q: d (e¬× In x) dx e-x e-x ln x – e-x e-× In x + O Option 1 Option 2 e-x e-* + X In x e-x +

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Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: ,1 .-2x +5 Evaluate | 3x 10-4x - 2y dy dx 25 3 25 26 7 27 5 28 3

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Q: 2) Integrate: S(29sinx + 6e + 5 cos x + Vx)dx

A: Given that, The integral ∫29 sinx +6ex +5 cosx+x5 dx By using ∫f(x)+g(x)dx =∫f(x) dx +∫g(x) dx ∫ 29…

Q: 5. fx² In x dx

A: See the details solution in below

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: -2 3. Integrate: [8x°e"-2 dx = du - e* 4x°dx 2 du = dex?. 4x° dx 4 3 2ou 8 ex".x°dx

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Q: 1- [(2x – 5)/3x – 1) dx | 2- S S(x3 – 10 + 3y² dy dx

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Q: 1. Solve (6re",x0 b. [3cos 2xsin 7.xdx

A: here we have to evaluate  a) ∫-11w(x)dx if w(x)=6x2ex3,x≤035x-3 , x>0b) ∫3cos2x sin7x dx

Q: Compute both dy/dx and d^2y/dx^2 if x^3 + y^3 = x.

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Q: How would I Find dy/dx implicitly 5xy + ln(x2y) = 9

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Q: 1. Evaluate : S (4x* + dx 2 S"(4x³ +)dx 0. x+1

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Q: Find dy/dx of 10x - 18xy2+10y3 = 48 9y-20x 3 (бу? -5ху) dy !! dx 9y-20x dy 3 (буз - 5ху) %3D dx dy…

A: topic - implicit differentiation

Q: 2 - S tần² (3x)sec²(3x)dx

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Q: /25-x2 V25-x2 -y2 1 dz dy dx -/25–x² -V25-x² -y²

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Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

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Q: (b) Integrate x-³e-l/a², dx

A: Here we can find the answer as below.

Q: 1. y = x3 – 2x² + 3x – 5 - - dy 3x2 – 4x + 3 - dx

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