19. f(x. y) In(1 - x - y) %3D

Q: s(VE + E dx

A: We want to integrate the given function.

Q: 11). If dy = (2x – 3) dx and y = 2 when x = 3, find the value of y when x = 5.

A: As per the company guidelines we are supposed to answer only the first question.Kindly repost the…

Q: Differentiate. y= In [(x + 4)(5x– 6)(3 – x)] d dy In ((x+ 4)(5x – 6)(3–x))) = |

A: Given: To find: The derivative of the given function.

Q: e 1 dx x/In x 1

A:

Q: 2dx J x (3(ln x)2 + 12 In x – 15)

A: The given integral can be evaluated using the factorization and substitution technique.

Q: 3 For y = 3x + x + 3 dy = -1 = dx

A: Given that:y=3x3+x+3To find: dydxx=-1

Q: 18. S V1+x dx 1-х

A:

Q: S S" x²cos(xy)dxdy

A: To calculate the integral: ∫01∫0πx2cosxydxdy

Q: 2 4 Evaluate Sx dz dy dx 3

A:

Q: dx 1. S 2x-x² dy 2. if y = x* (In x)? . dx 3. Sx³e-* dx .

A: We have to find the integration and derivative as asked in the given question.

Q: 1 d) S e) S csc³x cot³x dx f) S dx x2Vx2 + 4 dx

A:

Q: 26. Evaluate (x³ + y² + z)dx dydz.

A:

Q: dy Find for 3(x2 + y²) ² = 100xy dx

A:

Q: 2 / y xx lnx xy + y = In

A:

Q: Evaluate: e-y- [²" [m(x + y) - 7] dy dx In(x 0 x

A:

Q: -2x y" + (e by = 0 (e-* = z) -

A:

Q: dey こてxニコッン alx

A: We have to find :- d2y/d2x= ?

Q: 5.5 dy √y.evy 6. Š dx X+ e 7. fete d dx 8. fdx

A: Here we have to find the integral.

Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

Q: 8. ylnx – x In y = c - 9. y = ln (coth x) 10. y = sec³Vx

A:

Q: 4 For y = 2x* + x° + 6x + 1 dy |x=0 dx ||

A:

Q: X = e not inelude th degreo QUmbelin

A: The triangle is shown in diagram ,

Q: Use geometry to evaluate the following integrals.

A: Given: fx=2,0≤x≤53,5<x≤10 we know that ∫010fxdx=∫052dx+∫5103dx…

Q: OFind dy 9= (x²45x)"(x + Sec

A: The given function is: y=x2+5x4x+sec x5

Q: 4. If ( Inx dx = f(x)[In(x) + 1] + C, then f(1) = A 1 B D -1

A: Solution

Q: 1. S+1)dy y2+4

A:

Q: 4. (x +y- 4) dx - ( 3x-y-4) dy = o when x=4, y=!

A:

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

A:

Q: Cln S iny 7. ex+y dx dy 0.

A: I=∫1ln8∫0lnyex+ydxdy⇒I        =∫1ln8ey∫0lnyexdxdy               =∫1ln8eyex0lnydy…

Q: Veluate lesing Sub methad s x(xZ-3)" dX 1

A: Given query is to find the integral using substitution method.

Q: 35. If y=3x^2-x+1, find the point x at which dy/dx assume its mean value in the interval x=2 and…

A:

Q: 2 What is wrong with the equation dx =

A: Use the formula ∫xndx=xn+1n+1, to evaluate the indefinite integral ∫4x3dx.…

Q: 2 If "IF(x)dx=6 and frox)dx=7.50mm [rodr then f(x) dx = 5

A:

Q: 9. If dy = xy² and if y = 1 when x = 0, then when y = 3, x is equal to dx 0 -0 DIE

A:

Q: 17 (7+ x²^ dy when y = dx Find %3| 7 – x²

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Q: dy 1 3x2 In(x) + x³ • %3D dx

A: Given:

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 +

A:

Q: 2 4. S dy 1 y +y° - 3

A:

Q: 'a-x - dx atx valuate

A:

Q: 14. Evaluate y" or d'y of the function when x = 0. dx'

A: To find the y'''for the given equation 13x3+13y3=132  at x=0

Q: 5. fx² In x dx

A: See the details solution in below

Q: dx 1. S. 2x-x2 if y = x° (In x)? . dx 3. S x³e-* dx . 2.

A: Note : as per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find dy. y = In(1 + x4) dx 4x3 dx x4. 4x3 dx x4 +: dx

A:

Q: 9-y dy 5. S y

A: We will use trigonometric substitution.

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

A:

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

A:

Q: 2x(y+ 1) dx – ydy = 0 when x = 0, y = -2

A:

Q: Jar*dx = (1 +x*)y*dy

A: Follow next step

Q: dy y(ln y – In a + 1) dx 1 C = -ln C = -In Option 4 O option 2 1 C =-In

A: This question is based on solution of differential equation.