1 dx (36 – x²)3/2 1. + C 36 у36 — х? (x² – 36)3/2 + C A. 2. / *Vx - 36 dx В. 1 dx 1 х — 6 -In C. 12 x + 6 x – 6 3. V12x – x2 + C - 1 dx x2 – 36 | 4. D. arcsin 6 +C

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e %3D 5. (x2 - 1) dy =…

A:

Q: Select the correct antiderivative.

A: Given, I=∫11+x2dx

Q: 8x + 5 Split the integrand I dx into two parts. 8x + 5 dx 1 - x2 8x dx + 1 - x2 V1- x2 2x 8x + 5 dx…

A:

Q: 2) dx Ve -1 a) 2 vezr - 1 In (e – 1), c) arctan (e), d) sec-le

A: We need to solve the integral

Q: Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t =…

A: The objective here is to check whether Mean Value Theorem can be applied to show that at some point…

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

A:

Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

A:

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…

A:

Q: 1. sin x sin ydx + cos x cos ydy = 0 2. 3 ydx = (3x + 1)dy 3. (х — 2 у)dx + (2х+ у)dy %3D 0

A:

Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

A:

Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

A:

Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

A:

Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

A:

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

A:

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

A:

Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

A:

Q: (ylny-exy)dx + ( + xlny) dy = 0

A:

Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

A:

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: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

A:

Q: 1) y = Arcsin(1 – x²) 2) y = Arctan Vx² + 2x 3) y = Arctan /t²-1 + Arccsc t

A: Given : 1) y = Arcsin (1 - x²) 2) y = Arctan (√x² + 2x) 3) y = Arctan (√t² -1) + Arccsc t

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: (12z – 12z2 + 71z – 77 Integrate: 4x2 + 25 - la( |42° + 25|) – arctan X + C

A:

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

A:

Q: A particle is moving with S. H. M. while making an excursion from one point of rest to another, its…

A:

Q: (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy-5yzª dz

A: Find the value of function using integrate Compare the given expression with Mdx+Ndy+Pdz to obtain…

Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

A:

Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

A:

Q: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

A:

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

A:

Q: tion of the separable equation dy 23 3 +2)³ + 2)?

A:

Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

A:

Q: A point is moving along the graph of the function y=1/8x^2 +3 such that dx/dt = 3 cm/sec. Find dy/dt…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to t

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

A:

Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

A:

Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

A:

Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

A:

Q: 01 (test for exactness) * 4 points (siny - ysinx) dx +(cosx +xcosy) dy =0 01 (solve exact de) * 4…

A:

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

A:

Q: dy = (1+3 siny)2xdx

A: We will solve differential equation using variable separable form

Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

A: