3. Find the derivatives of the following in two ways: -by evaluating the integral and differentiating the results, and - by applying the first fundamental theorem. sin x d b. dx d cos tdt [3*dt а. dx

Q: 8. Find the general indefinite integral (x³ -2² + x)dr; b) / (2" +-)dr, x > 0; c) (sin(3t) +…

A:

Q: 11. Evaluate the following integrals. sinx dx 1- cosx dt fxsec' x dr b) a) c) t2 +81

A:

Q: Find a linear differential operator that annihilates the given function. 2.3 + e* cos 2x

A: Let, the given function:fx=3+excos 2x

Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…

A: Let y = sin (x)

Q: find a linear differential operator that annihilates the given function. у 3x sin(3x)+ Зхебх у%3 езх…

A: We know that the annihilates polynomial of sin(ax) & cos(ax) is (D^2 + a^2) And the annihilates…

Q: Use Laplace transforms to solve the following differential equations. (5) y" – 2y = e' sinht with…

A:

Q: Find the Total Differential of each of the following functions. 12. Vx2 + y2 13. (x2 – y2)3 - 14.…

A:

Q: The differential equation 3zy" – 2y + 7y = tan x is normal on any open interval not containing = 0.

A: The main objective is to determine the given statement is true or false.

Q: Find the Total Differential of each of the following functions. 12. x2 + y? 13. (x² – y?) 14. sin-…

A:

Q: The following ordinary differential equation is given: d^ 2u /dx^ 2 + 6 du /dx – u = 2 At x = 0, u…

A:

Q: Consider the following. sin (18.35)* + (7.657) – sin(s² - 8°) Find z = f(x, y). f(x, y) = Use the…

A:

Q: Calculate the following definite integrals. -1/2 1 dx "dx dt (t+2)³

A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

Q: Find integrating factor of the following differential equation sinx ay = sin*x+(cosx)y dx a. -cscx O…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = cos 4x

Q: 2m 28. t sin 2t dt

A:

Q: Use Laplace transforms to solve the differential equation de +4-+ 40 = sin (8t) dt d? given that 0…

A:

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: u (x…

A: The Volterra integral equation is given as u(x)=x22-∫0x(x-t)u(t) dt. We have to solve the equation…

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Find a linear differential operator that annihilate the given function d) Sin5x + 10 cos5x e)…

A: (d) Given that y=sin5x+10cos5x We have to find a linear differential operator that annihilate the…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: If L is a linear differential operator with constant coefficients and f is a sufficiently…

Q: Q1: Verify that the given functions are solutions of the corresponding integral equations by using…

A: Given: ₵(x)=xex and ₵(x)=exsinx+2∫0xcos(x-t)₵(t) dt

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Sin (x-t) u(t) dt = 1- Cos x

A:

Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

A:

Q: 13. Find the differential dy for each of the following. a) y = cos 2x- sin 3x b) y = x2 – V36 – x² |…

A:

Q: 2. The exact differential d xdy - ydx what is the d(xe")= x?

A: Let's find.

Q: (A) Find the general solution to ONLY ONE of the following differential f ations (1) (sec(y))² y' -…

A: We solve the given ODE  (sec(y))2y'-3tan(y)=-1 ......(1)

Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: 9/u The evaluation of the Integral of S° sin2x cos4x dx is

A: we have to integrate

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: Let x and y be differential function of t and suppose they are related by the equatin xy-1=y^2. Find…

A: Differentiating with respect to t, we get

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: (2) Find the differential of each of the following functions. In other words, for each of the…

A:

Q: 1. Determine the following indefinite integrals: S (Ax-1 - Bx-3 + Vx") dx a) ez (wt) – cos(Ewt) )…

A: A=2.6, B=6.4, C=2.6, D=3.4, E=2.7 To find:-

Q: 2.2 Evaluate following integrals. .sin VT cos E 2.2.1 dx

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: 1. у" + 2y' — Зу %3D sin(2x), У (0) %3 у'(0) — 0 |

A:

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: We have to find a linear differential operator that annihilates the given function.

Q: 1.Evaluate the following integrals and check using differentiation: d 5-5t dt 10 +2.12e- . (a) 0.5t…

A:

Q: 15 Evaluate the integral (10 + sin t)" cos t dt using the substitution u = 10+ sin t. + sin t) cos t…

A: We are asked to evaluate the integral.

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration