Show that the value of Vx + 8 dx lies between 2V2 - 2.8 and 3.

Q: v°dx + x (x + v) dv = 0

A: Let's find.

Q: JVVy+1-2 dy can be evaluated conveniently if we let x =VVy+1 - 2 and dy = 4x(x² +2)dx. (A True B)…

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Q: The value of the integral | (|x+1|+|x) dx is а) 9 b) 1 c) 0 d) 4

A: The given integral is  I=∫-22x+1+xdx To solve the given integral we need a result that is ∫x…

Q: 6. | f(2)da = 3, | f(x)da = 9, Suppose | f(2)dz = 1. %3D | f(x)dx = | = (3f(x) – 9)dx %3D

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Q: (х + у+4)dx+ (x + у—3)dy %3 0

A: The differential equation M(x,y)dx+N(x,y)dy=0 is said to be exact if there exists a function f(x,y)…

Q: To answer the following questions, suppose that Só f (æ) dx = 4 and S s (2) dz -6.

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Q: 1 By using completing the square , dx can be rewritten as /x²-4x – 7 1 VTr- 2)²– 3 1 =dx V(r- 2)? +3…

A: We need to write the following integral by completing the square   ∫1x2-4x-7dx

Q: Answer the following neatly and completely. Find dy/dx. 1.y = 2x4 3x2+2 2. y = 53x2-2x+2 3. xev + y…

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Q: What is f P-(x)dx if the given DE is y(6y2 – x - 1)dx + 2xdy = 0?

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Q: (Answer the ff. and show the solution) Evaluate: et 1. S dt 3 (e2t+8et+7)z 1 х—1 2. S. 0 x²+3x+2 dx…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: Find | (V – 6e") dx, where A > 3. Answer choices have been slightly simplified

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Q: u = Vx + 5 (x + 1) then du/dx is Зх — 11 Зх + 11 2 Vx + 5 2 Vx + 5 A 3x + 10 Зх — 10 2 Vx + 5 2 Vx +…

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Q: d | Vsint dt dx 3 2.

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Q: The solution of (v + x + 5)dy = (v - x + 1) dx is

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Q: 2. Given that y = (a + bx)e-* where a and b are constants, show that +2 +y = 0 dx2 dx

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Q: | f(x)dx = 12 and f(x)dx =3.1, then J f(x)dx =

A: Use formulas of limits of integration

Q: Evaluate fo (36 – z') (1 – 2*/3) v36² x2 dx -

A: Solution is here

Q: S(-0) dx = - 4 In|x| + C 8. 2. )dx = 6 Vx + C

A: ∫x4-dx=x28-4ln(x)+CApply the Sum Rule:…

Q: dx V2x-x2 /2х-х2

A: Evaluate ∫42x-x2 dx

Q: Evaluate 2x+4 1. fx e**dx 2. SInx dx 3. J x2-2x 4.(a) (e* + 1)2 dx, (b) Sx³e2x dx.

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Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: dx J. (3+x²)$/z

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Q: Q3. Find dt 4x – 2 dx x² + 20 4t

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Q: Suppose that (x) dx=3 and g(x) dx=7, then what is 1 8. 8 the value of (х) dx ? 1

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Q: Show that dC 1.8x - 1.5 - dx Vx2+0.04 and hence determine the value of x that minimises the cost

A: if for a function f(x) at x=a ,f'(x)=0 then we check for f"(x) if it is positive at x=a , then f(x)…

Q: 13. Se"dx = %3D 3a41 re +k. 3x+1 B 3e" + k. A c+k. 3x te +k.

A: ∫e3xdx=

Q: Find dy/dx y = Vx' +3x4 +4 %3D e X• Sm (5x) onvue

A: We need to find dydx=x6+3x4+4 First, consider y=x6+3x4+4 Now, we will use the chain rule to find the…

Q: d sec(11x – 4) dx = dt 13

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Q: If f(x) dx 37 and (x) dx = 14, find [4f(х) + 69(х)] dx. %3D

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Q: If f(x)dx=10 and | (x)dx=3, then | f(4 – x)dx=? %3D

A: Given that: ∫-26f(x)dx=10 and ∫26f(x)dx=3

Q: Find -dx et + x-2 + C ex 1 + C 1 + C (1/2)x² e* e* – In |x| + C

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Q: 3x 2. S dx Jx2-x-2

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Q: Given that 7 < f(x) < 8 for 1 < x < 2, | f(x)dx estimate the value of / s(x)dx < VI

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Q: What is the antiderivative of -dx? A 6x2 1/3 + C ® x/3 (2x% +9) + c %% + 6r/2 + c /2+c

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Q: If F(x) 2 3x3 is an antiderivative of f(x), find / (-3f(x) – 4x³) dx.

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Q: 8. If f(x) dx 31 and %3D g(x) dx = = 14, find [3f(x) + 4g(x)] dx.

A: use given integral for finding the  value .

Q: (x) dx = 6 and f(x) dx = 10 , then +3] dx = %3D 2

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Q: h. If fS(x)dx =18, then f(S(*)+4)dx = %3D %3D b. 2. If [f(x)dx =a + 2b , then (f(x)+3) dx =

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Q: d V3i dt = dx x²

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Q: If y = = e2a + e3x, then d y at x = 0 equals dx3 %3D

A: Given: y=e2x+e3x

Q: 8. If f(x) dx = 10 and f(x) dx = 3.7, find %3D f(x) dx. Answer:

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Q: (b) Given that, V2x + 1 and y = 1, when x = 12. Express y in terms of x. %3D dx

A: Topic :- Differential equation

Q: 4 | f(z)dx 14 what is 3 | f(2)dz? Given that 4 answer

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Q: dx Find So 13 V(1+2x)²

A: Let I=∫013dx1+2x23 find out the integral value of I

Q: Use integration by parts to evaluate |6xe* dx. (7x+1)(6e*) +C A) бе 49 B) -7x e +C 7 | C) (6e"*) -7x…

A: givenI=∫6xe-7xdxif u=x and v=e-7xthen we use integration by parts Formula∫uvdx=u∫vdx-∫[ddxu∫vdx]dx+c

Q: Find the antiderivate of dx/(x2+4)3/2

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Q: „5V7/2 V 25 – x2 xy dy dx + xy dy dx dr de = Jo

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Q: 4 d 4. Find dx 2 Vt2+17 dt

A: The given integral is,

Q: If f(x) dx = 33 and g(x) dx 14, find [4f(x) + 5g(x)] dx. P Type here to search

A: We have to find