sin x +x) dx Acos² x S(sin t + t) dt 8 dx cSC X

Q: Find the antiderivatives of the functions: 1 f(x) = x* – 2x² + sin x a. Зx3+Vx+1 b. h(x) =

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Q: 1) Evaluate the following (general) antiderivatives: a)[9x' +7x+4 dx = b)J9 cos(x)+8sin(x)+7e*…

A: a) ∫9x7+7x+4 dxb) ∫9cos(x)+8sin(x)+7ex+6sec2(x)+4x-31+x2 dx

Q: Find an antiderivative of the function. ..... (a) h(q) = sin(q) %3D H(q) - Cos g +C %3D (b) f(x) =…

A: We have to find derivative

Q: Given f(x, y) differential df = 10x?y then the total O 20xy dx + 10x² dy 20x dx + x2 O 2xy dx + x²…

A: For the solution follow the next step.

Q: Perform the following integrations: 1) y' = 5e% sin (e") → y= +C x +1 2) y' x2 + 2x + 4 +C 3) y' =…

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Q: dy Find for the following functions: d.x (i) y = 5sin(3z²) (ii) y = ezVz² +1 (iii) y = (tanh-' (V#²…

A: Given function is: y=5sin3x2 Differentiating with respect to x we get, dydx=6x ln 55sin3x2cos3x2…

Q: Find the general solution of the following DE by finding an integrating factor to make it exact…

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Q: dy : Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh x

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Q: 5. S 2x' dx 6. S*-5x* dx x3

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Q: B sin x 4. Find an antiderivative F(x) of the function f(x) such that F(0) = 1. y + cos x

A: Given function f(x) = β Sin x γ + cos x   such that F(0) =1The antiderivative of the function is…

Q: Find the particular antiderivative that satisfies the following conditions: dx/dt=8e^t−7;…

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Q: Find the most general antiderivative. S(-6 cos t) dt 6 sin t + C -6sin t + C -6 + C sin t sint + C

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Q: 1. The function ø(y) = y¯2 is an integrating factor 2y(x + y + 2)dx + (y? – x2 - 4x - 1)dy = 0.

A: We have to check given differential equations is exact or not

Q: g(x) = sin(t? + 1)dt

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Q: "valuate the following integrals using substitution(s) 1. S 2x(x² + 1) 23 dx use u =x + 1 2. [4e5*…

A: The integral formulae are ∫ddxxn=xn+1n+1+c∫ddxeax=eaxa+c

Q: Given: x+5 The provided integral: dx V9 – (x – 3)²

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Q: Match the function on the left to its appropriate antiderivative on the right. Prompts Submitted…

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Q: Find the most general antiderivative of the function. 1+t+t? a) g(t) = Vt b) h(x) = 2x + 4 sin(æ) c)…

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Q: Find the following antiderivative: 4. /(arctan r) dx, by using the substitution u = arctan x

A: Find the following antiderivative by substitution method

Q: Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. y(y² + 1)dx…

A: (1) The given differential equation is: y(y2+1)dx+x(y2-1)dy=0ydx-xdy+y3dx+xy2dy=0Divide both sides…

Q: Determine the following general antiderivatives. [3x (x²-5)³4x [Axe+²7 tan(+²7) dx 10 d. cos(x)…

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Q: Find dy/dx for the following function:- (1) y= In(r+4)-xtan (4) y x*+1) (2) xy +xy x+ 3y (3) Iny e…

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Q: Use either integration by substitution or integration by parts as needed to evaluate S³= A B x²+1…

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Q: Find the general antiderivative of f and check your answer by differentiating:   f (x) = ex − 4 sin…

A: Find the general antiderivative of f and check your answer by differentiating:   f (x) = ex − 4 sin…

Q: x +1+ tanh² (1) dx (a) x2

A: We have to solve the problem

Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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Q: (ylny - e¯xy)dx + ( + x lny) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact differential equation. If it satisfies the…

Q: Compute for the general antiderivatives of the functions 1. S(x – 2)? dx 2. S(2x + 3)³ dx 3. [ sin…

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Q: By Variable Separable 1. x?dx + y(x – 1)dy = 0 2. x²yy' = e'

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Q: Find the antiderivative F(x) of f(x)=12-pi(sin(x))+17cos(x), given F(0)=3pi

A: To find the anitderivative of the given function.

Q: Find dy at x=0 for each part below. dx x sec (ax + (here the answer should be in terms of a and b,…

A: Differentiate wrt x

Q: Evaluate the following (general) antiderivatives: a)f9x - 7x+8 de 6 b)|2 cos(x)+3sin(x)+4e*…

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Q: 9) xdy- ydx = (x² + y²) e* dx

A: Let's solve given diffrential equation.

Q: Find f. (Use C for the constant of the first antiderivative, D for the consta f"'(t) = Vt - 3 cos(t)…

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Q: Find the following antiderivatives. a. ∫(3x^4-cosx)dx b. ∫(5^3sqrt(x^2) + 2x-1)dx c.…

A: ∫xn dx = xn+1n+1+C. ∫ax dx = axloga+C

Q: Q2: find the antiderivative of the following a) S x + e* + sec(x) tan(x) dx b) /블dx x+1 c) S(e* + +…

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Q: 181. y = (x + cos z) (1 – sin z sz)(

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Q: Find the general antiderivative of f(x) = 4 cos (x) – 11 sin (x) and check the answer by…

A: given that:       f(x) = 4cosx - 11sinx we have to find first,   ∫f(x)dx then after we have to show…

Q: find dz/dx and dz/dy for the following expression z =  tan-1 [(x+y)/(1-xy)]

A: This question is based on diffrentiation of function.

Q: Find the general antiderivatives of the following functions: 7x dx a. (1-x)* (1-x2)3 b. S(6 sin x –…

A: To find the general antiderivatives of the following functions

Q: 3. Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. a) y(2xy…

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Q: Find the antiderivative that satisfies the initial given condition. f"(x) = 2e" + 4 sin x, f(0) = 0…

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Q: 6) 3x²y dx + (x² + y²) dy = 0 3

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Q: Of Find the general solution for the following first order D.Es? (Answer two only) sinx+cosh 2y-…

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Q: Find the value of df/dt for the following function: F (x, y) = xy² x= cost, y sin t.

A: We need to find the value of df/dt for the following function: f(x, y) = xy², where x= cost, y =sin…

Q: 1. Given xy = sin x , show that d'y 2 dy +=+y = 0. dxx dx

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Q: Match each general antiderivative with its rule xn+1 а. dx n + 1 dx, n + 1 b. (п + 1)2^+1 С. dx…

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Q: It is definend as (Tf) (t) = S sin?(x – t)f(t)dx ,with fe [0,1] 1) is T: c [0,1] → c [0,1] defined…

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Q: (a) y = (6x² – 8x + 15)5

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