nd the antiderivative x² + 2x -dr. (r² + 1)'

Q: 2x e d.x 4e2 – 8e" + 5

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Q: y dy J 725 – 16y 2.

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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: •Cx²+Jy'tuxy X y(2)21 use Rennoull EQ.

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Q: x – 8 dx x² – x – 6

A: Find the integral by substitution method

Q: constant

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Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: x4 + 15x2 + 3 dx x5 + 25x3 + 15x

A: Topic = Integration

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: Find dy for the given values of x and Ax. y = 2x° - 7x; x= -2 and Ax= 0.2 dy =D %3D (Round to the…

A: We have to find the dy

Q: Find the most general antiderivative. dx x2 A 2- +C В с © -2.c (D 2

A: topic - anti derivative of  a function

Q: dy A. Find for the following: dx y = Vx3 +- In(esinh¯ x) i. x8

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Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: S: dx V4 + x² (a)by parts, letting dv = dx V4 + x² (b)by substitution, letting u = 4 + x2 3.

A: Integration basically means to find the integrals, i,e. to assign numbers to function in such a way…

Q: dx 2xVIn x (b)

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Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Integrate the following using substitution 1) z5 (9z6 – 7)8 dz 2) S dy 4 y3 2-5y4

A: Given that: 1. ∫z5(9z6-7)8dz   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: dy when t = 7. dx 13. Evaluate y = 2z? – 3z + 5 x = 4t' +t t = z? + z+1

A: Derivative of the function decides whether the function is increasing or decreasing. If the first…

Q: dy Differentiate implicitly to find 6 5 3) x y+9x = 6y +4 dy

A: A detailed solution is given below

Q: x* )!' dx + ی 3 4 11

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Q: dy olve the O.D.E’S y + 4 = 2x using separable of variables. dx

A: Here is the solution:

Q: Sove for dy 4 X3 hy= e*csch (2-y?)

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Q: dz = 2ni to deduce that z+1 Use the fact that (x+1)dx+ydy Sc O (x+1)dy-ydx = 0 and Jc (x+1)²+y² =…

A: Given ∫c1z+1dz=2πi ......(1)we have to prove that ∫c(x+1)dx+ydy(x+1)2+y2=0 and…

Q: Find the total differential. z = 8x4 8x4y10 dz = (No Response)

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Q: dy Given y x" In (2x), determine dx ax"- In (2x) + a-1 a.a"- In (2x) + 2.x O...n 1 None of these ax…

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Q: Find the most general antiderivative, (5e 3x -4 e-X) dx

A: Integration of the function helps to find the required value of the given expression. Integration…

Q: Find the total differential. 4x + y w = 2z - 8y |

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Q: Find the antiderivative of dx/(49x2+16)2

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Q: Find the total differential. 2x + y W = 5z - 4y

A: For a function of two or more independent variables, the total differential of the function is the…

Q: Find the antiderivative dx/(x2+4)3

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Q: • ["* [*, [° 42²y — 2²³ dz dy dz J1 1. Evaluate

A: NOTE: As per our guidelines, I have solved the first problem. If you want the answers of rest,…

Q: Find the antiderivative dx/(49x2+16)2

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Q: €x2 + 5х + C) dx %3D Зх + 5

A: Given: ∫32x2+5x+Cdx=3x+5

Q: Find the total differential. z = 10x4y5 dz = (No Response)

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Q: y(x), find y(4)]. S 4xy' – 4y = 7x, ly(1) = 4.

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Q: Q2: Sdve the differential eqpeation d²y =20"t 9Sin 2x -2Cos 2x %3D

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Q: Q2- Reverse the order of the integration ff dy dx + f2f²dy dx equal:

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Q: Find the antiderivative of: ii x2 iii 5 iv r-2 x-4 vi xt vii V b From your answers in a, predict a…

A: To find: The antiderivative of the the given expression. Concept used: An antiderivative of the…

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 x3 (i) dx (3–2x)5

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

A: Given, u= ∫dx/(4+√x) We can solve it by substitution method.

Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: Find the total differential. 5x + y w = 2z - 6y dw =

A: Consider the given equation. w=5x+y2z-6y The objective of the problem is to find the total…

Q: dy You need not expand your answer. dx Calculate y = (7x0.5 – x2)2

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Q: 8e" Let g(y) Y + 8 dg Determine dy

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Q: Find h t Trans form of decivative for d²f and d' f dt3

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