1x x2 SI x +1)dzdydx 00-y2

Q: + 1 =2e- dy

A: Given, Can be rewritten as

Q: Find the antiderivative of xe2x/(1+2x)2 from 0 to 1/2

A: Given the integral ∫012xe2x1+2x2dx

Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

A:

Q: dy de Xoy. -Secxy)

A:

Q: L,sgn(x) dx = 1. 0 2. 2 3. -2 4. 1 2 O 1 3 O 4 O

A: (1)…

Q: 2dx J = (3(ln x)² + 12 In x – 15)i -

A:

Q: 2 (Dx-2Dx0y +Oy)u= 3Xy %3D AMS. 4

A:

Q: (b). Evaluate the integral 6x Vx +4 dx.

A: Part(b) Given

Q: 1. ²₂(x² − 2xy² + y²³) dx dy

A: Solve the following integration .

Q: 2ху ni V1+ x2 dy 2xy dx

A:

Q: 2x y3= Ked dy

A: First take the log both sides and simplify than differentiate with chain rule.

Q: -8 1 The integral dx x2 + 64

A:

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

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

A:

Q: . Evaluate using integration by parts 8. (5x - 3) sin(12x)dx = TC 6.

A:

Q: te the Integral. 1 xV1- x2 dx 14

A:

Q: Evaluate the iterated integral. * 2y (6 + 8x2 + 6y²) dx dy

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Solve the ODE: dy (x' +4x) 0 using separable variable method: dx x(sin 2y +4)

A: The differential equation is as follows : dydx-(x5+4x)x(sin2y+4) = 0 Hence we get dydx =…

Q: Evaluate the double integral: 2 √ ² √² (3x² +9y²) dx dy 0

A: To solve the given double integral.

Q: dz %3D dt

A: Given that: z3=x3+y2, dxdt=2, dydt=1 and z>0.

Q: (1+ ye* + xye")dx + (re" +2)dy = 0 %3D

A: We will first show it is an exact differential equation

Q: Find the integral 17T dx 2+18 1 는시17x + 18+c 17 1 18x - 18 +c b.

A: Solve by substitution integration method

Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

A:

Q: Solve the problem by using Exact DE 3 1. (2 x³ x y² - 2y + 3) dx − (x² y + 2 x) dy = 0

A:

Q: y" + 4y = 2 sin(6x)+ 6x²e¬3z + 5x,

A:

Q: 7(x2+yZ dx+Zxy dy)

A: Given: - The differential equation is, 7(x2+y2dx+2xydy)=0 To find: - The solution of the given…

Q: 1) CSc y di + secx dy =0 CSC y Y.

A: Given query is to solve the differential equation.

Q: dx 2 (1+3x)2

A: We will find the integral as following.

Q: y et 2x *Sec2X Pinel dy o

A: By using these differential formulas that are ddxex=ex, ddxax=axlnx where a is constant,…

Q: Solve using product rule d(uv) = u dv + v du: f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given that, fx=x2+4x4-4x2+16 Differentiation formulae: ddxuv=uddxv+vddxu    [Product rule]…

Q: 2dy+ydx=y3(x-1)dx (Bernoulli)

A: We have to find the general solution of differential equations

Q: dx 2 28 — 12х — х

A:

Q: 2 1) (-2xy) dx + ( Sing-x²) dy

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

Q: a) dt 9 =dx xVln x b)

A:

Q: 4. Evaluate the integral 3x2 + 13.x + 11 dx I (x+1)(x +2)²

A:

Q: dy Find in terms of a and y if æ In y + y° = 6 ln x. 3 dr

A:

Q: Given the integral 6x2 + 10x + 9 dx -2

A:

Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: 29 у %3D sec y/x + y/x; у(2) п

A: y'=secyx+yx:  y(2)=π.

Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: 4 dx L 11. 1 + (2x + 1)2

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: ylany +1) dn -xdy = 0

A: y(2xy+1)x=dydxdydx=2y2+yxdydx-yx=2y2this eq is of the form of  bernoulli D.E dydx+P(x) y= Q(x)…

Q: 2 x²e¬2® dx. Compute

A:

Q: Solve the LDE of dy/dx = [1/(1+x3)] – [3x2/(1 + x^3)]y

A:

Q: 4- XLnx dy dx +y=zLnx

A:

Q: 1 y2e- dy 7 صواب ihi

A:

Q: Hiw 2 4t é dt 2 O Sx Sečx dx

A: (1) Consider the given integral. I=∫csc3dx The reduction formula is defined as.…

Q: 4 d 4. Find dx 2 Vt2+17 dt

A: The given integral is,

Q: rtan r d Vt3 +4 dt dx 1/a

A:

Q: Show that the antiderivatives are equivalent.…

A: ∫6/(4 + 9x2)  dx = arctan 3x2 + C or arccsc √(4 + 9x2 ) / 3x + C We need to show that the…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.