(-1)" S. =È D n=1 Vn +1

Q: zy dy de t 5/2/2/0

A: To evaluate : ∫032/2∫0xxy dy dx+∫32/23∫09-x2xy dy dx The general formula of integration is…

Q: dx = [Af(x) – B In(g(x))% + D S and if A =.B < 0 , then ƒ 2 dx = x+2 x+2 ...

A: The given integration: ∫abx2+x+12x2+2+x3+x dx=Af(x)-Bln(g(x))ab+D∫abdxx+2  →  eqn 1 From the above…

Q: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

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Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: dx from a = 0 to b = 1 et + e-

A: Integrals in some cases can be simplified to standard integrals with relevant substitution. For…

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: Calculate MN and TN for the value of N indicated.

A: Given ∫12lnxdx, N=5

Q: calculate SN given by Simpson’s Rule for the value of N indicated.

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Q: d. Use your answers for parts a and b to estimate 1 -dx using the trapezoid rule with n=4

A: Approximate by trapezoid rule

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: 1. So letet Jo 1+ e* t -dx

A: The given integral,        ∫01ex1+exdx

Q: die ktvaate et:rlrs erziv. 2l y=a* + &r-- 5+e" Kl) =

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Q: So Simz So e" dz dy dx uate: e + Vē – 1

A: Please refer to the image below

Q: 100 e of f (s) = %3D s (s+2)2(s+3)

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Q: 4 dx 1+ By using (Answer one only) a- Trapezoidal rule when n=5 b- Simpson's rule when n=6

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Q: --- Q#3 Evaluate Cf 2x dV →Where E = {(x, y, z)| 0sys 2,0sx sV 4 - ,0 < z y} ,0 sz< y} Ee

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Q: Solve the following problem Pu + dx2 = 0, 0 < x < L, 0 < y < H ду? ди ди (0, y) = 0, (L, y) = 0, dx…

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Q: How would I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

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Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: d Suppose a e R, where a > 0, a ± 1, what is - dz

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Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: Given that S" 4Væ dx = 152, what is fo*4Vt dt ? 3 )

A: As we know that;  the value of definite integral will not change if independent variables changes,…

Q: d Suppose a E R, where a > 0, a ± 1, what is- - [a*]? dx

A: We need to find ddxaxwhere a&gt;0,a≠1

Q: D. (a)S sec? 3x dx (b)S 2cosec2 4t dt 2cosec24t dt

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Q: What is the choice of substitution for S e*(1+e*)(1/2) dx?

A: The given integral,        ∫ex1+ex12 dx

Q: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

A:

Q: Vēt VE dt

A: Our Aim is to evaluate the integral given below:-

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

Q: S dy S f(x, y)dx

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Q: Q2: Evaluate o o" y*(x² + y²)dx dy 1 cV1-y? y² (x? + y?)dx dy

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Q: i)S V+ 3. + e dy

A: We have to find the integral of given function .   Here student asked only one question so that i am…

Q: 6. Write.a.Ct).in. the farm..aaT.T+ a. N. a..r(t).=(tcost). .+ (tsint.) j.+t ..to.

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Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

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Q: dy x fanx

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Q: b) sol v e in e Iknear di tteren tiaı hrst oroer equanon dy 2. り = n2 cosh cen), when り (1)

A: The given differential equation: dydx-2xy=x2 coshex ;          y(1)=0

Q: (a) Evaluate by solving the work for (i) Sxe-*dx.

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Q: ne exact length of tne X = Vy (y – 3), 4sys9

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Q: - [Mesin(2x) dx = esin(2x) + C_then the Mis equal to +C,t

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Q: 27 dz, C: z(t) =t – ti, t e [-1,5].

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Q: (1) So“ dx let t=x o Vx

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Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate ſ,(x3 + 1)dx.

A: To find: ∫-11x3 + 1dx using trapezoidal rule with n=4

Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: dy Find dæ |(7,9)=(-1,-1) if e sin (x? – xy) = y² – 1.

A: Given,          xsinx2-xy=y2-1

Q: dy If y = tan 1(Ve*), then dx Select one: a. 2(1+Ve*) b. 2(1+e*) ex C. 2(1+e*) ex 2(1+Ve*)

A: Given y=tan-1(ex)We know that arctan(u(x))'=1u(x)2+1*u'(x)=1(ex2)2+1*ddx(ex2)=ex2*12*ddx(x2)ex+1

Q: n + 1 Σ' n=1 n² Vn

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Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: 1- y? 1+ y 4 06: If x? dx Show that 1 %3D ,2 dy レアス+1.

A: