Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.) f "(x) = 10x + sin(x) f(x) =

Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: Evaluate.cuse C for the Constant of integration). 40 t6x-X dx

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Q: . (solve exact de) (2ysinxcosx - y + 2y?e*v* )dx = (x - sin?x - 4xye*)dy

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Q: Find the particular solution for (2y - x) dx + 3xy2 dy = 0 when x = 1, y = 1

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Q: Let y = 4x2 + 4x + 3. Find the differential dy when x = 1 and dx 0.4 %3D Find the differential dy…

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Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x³–2x)* 1. у- ; d'y/dx? 2. Y = (5x³ + 2)6…

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Q: Write the general antiderivative. (Use C for the constant of integration.) x2+1 dx 5x Need Help?…

A: The integral of ∫xndx=xn+1n+1.

Q: sinh x – 1 dx cosh x

A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

Q: 2, t'y"+ty'+y= Cos(int)

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Q: se C for the constant oT integration.) (7 cos x + 3 sin x) dx

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Q: f(x) = 9x3 + 4x.   Find the differential of the function.   dy =?

A: Given , y=fx where fx=9x3+4xwe have to find the differential dy

Q: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: Find the differential of the function y = f(x) . f(x) = (5x² + 7)/3 dy =

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Q: B) Find for the Implicit function: dx x2 - sin(xy) + y² = 5xy

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Q: Let y = f(x), where f(x) = 6x2 + 3. Find the differential of the function. dy =

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Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: Find the antiderivative. (Use C for the constant of integration.) (8x + 9) dx

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Q: The general antiderivative determined by - x² - 3x +2 is dx

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

A: Given that

Q: Using dx/dy solve sin(x+y)-cos(x+y)=1

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Q: 2. If y = x +3x-2x+1, find the values of the following e. derivative, i. У"(2) d'y ii. dx ii. y" (2)

A: Please refer to the image below

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: Find the most general antiderivative of the function. ( Use C for the constant of the…

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Q: Solve for the differential of y when y=sinxx• x=-. and dx= 3 4 2

A: i am going to solve the given problem by using some simple calculus to get the required result.

Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: Find the antiderivative of f(x)=cos(3x)

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Q: of

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Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: dy dx || X x² + 100

A: We have given differential equation  dydx=xx2+100 dy=xx2+100dx Integrating both sides…

Q: 53. df = (x+ 1)ye"dx + xe*dy

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Q: For the function f(x) = 2 sec (2x) tan (2x) + sin(x) + cos(x), find the most general antiderivative…

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Q: FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 1. Z=- ; d²z/dx? 1+x2 2. Y= (3x³ + 2)ª ;y" 3.…

A: z=2(1+x2) Differentiate with respect to x, dzdx=ddx2(1+x2)-1      =2(-1)(1+x2)-1-1(2x)…

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Here we can use the following formula  If z=fx,y, thendz=fx dx+fy dyδzδy=fx δxδy+fy

Q: cos xdx (vii) S 5+sin2 x

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Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: Write the general antiderivative. (Use C for the constant of integration.) 29e2.9x dx

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Q: Find the antiderivative of the given derivative. dp dx ex+ 2e-2x (ex - e- 2x) 4

A: Given dpdx = ex + 2e-2xex - e-2x4

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

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Q: We know that x =r cos 0 and y =r sin 0, then find the derivative af /ər if 1 f = x2 + y2

A: Given f = 1x2+y2  and x = r cosθy = r sinθ Thus f = 1r cosθ2+r sinθ2= 1r2 cos2θ+r2 sin2θ=…

Q: dx - is 2/x - Sin| x +s|+c. Vx +5 The antiderivativeof - A) True B False

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Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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Q: B4. Evaluate e* sin x dx by using integration by parts method.

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Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

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Q: Find the antiderivatives |x In(x²) dx + sec? x dx CO X dx sin5

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