2 Evaluate f(x) dx, given that f(x) dx = 6.

Q: 3.b) Evaluate the DE * 3x(xy – 2) dx + (x³ + 2y)dy = 0

A: Given that: 3x(xy-2)dx+(x3+2y)dy=0

Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: -(3x² + 10)e¯= d Evaluate dx (3x² + 10)e¯ª at x = 0. d (3x² + 10)e dx x=0 II

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Q: Calculate d2y dx2. y = e−(x − 3) − x

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Q: e 1 dx x/In x 1

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Q: 2- e dx 十e X X e dx 2.

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Q: 12. Given: f(x)dx = 4 S(»)dx = -1. and Find: (a)

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Q: Evaluate dy/dx at (-3,1) for x3+(7+xy)5/2=82/3+y2

A: Given:

Q: 21 11 | {(=) dz f(x) dx = where a = and b =|

A: Given: ∫821f(x)dx-∫811f(x)dx=∫abf(x)dx   We know that ∫acf(x)dx= ∫abf(x)dx+∫bcf(x)dx We can write by…

Q: dx dx Therefore, 1 f '(x) = 1 + 1 + (x - 2

A: Solution is given below....

Q: what is the derrivative of y^3 + y^2cos(x) = x^3 -3x and what points in the function for dy/dx does…

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Q: Find the value of df-1/dx at x = f(a). f(x) = x 2 - 5x + 6; a = 5 1 1 10 1 15 O 5

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Q: 8. 4S f(x) dx = dt 9. S f(t) dx d 10. dx | f(x) dx = a

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Q: (c) [ n@dx In(x) dx x2

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Q: 1 What is S dx? x²+2x+5

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Q: 21 (e) If(x)| dx (f) f(x) dx 16

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Q: xdx g) 7x + 2) h)f sin(In x) dx of xe" dx

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Q: S f(t) dx = 0. 1.

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Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: 1-f e*. Inx dx

A: Given :  ∫ex lnx dx  To find : we have to find the Integral for given expression.

Q: 3. Differentiate y = 2x-1 - with respect to x and then evaluate 2 x(x – 1) -dx (2x – 1)2

A: Given and

Q: 11 f(x) dx - 3 I f(x) dx = f(x) dx

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Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)

Q: 4. If ( Inx dx = f(x)[In(x) + 1] + C, then f(1) = A 1 B D -1

A: Solution

Q: 1. Find ƒ (x) dx given [² f(x) dx = 2 and ₁² f(x) dx = 3

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Q: +y Evaluate dz dy dx 20 3 0 -3 0 00 -10 -4 0 10 -2 0

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Q: @[² (d) √x-x (x² + y²)³/2 dy dx.

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Q: Evaluate the function: S de x(x-2) -dx (x–1)³

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Q: 27. Select the correct one SEF (x)dx S% \f(x)\dx, | - Sif(x)dx < S%\f(x) |dx,

A: Given- Consider the all options given below, To find-  The correct one in the above options.

Q: e" sin x = x- xy S1

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Q: x - 3 7. S V25- (x-2)2 dx 8. S tan5 (2) dy

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Q: f cos 4x dx 2x dx S (x-2)²(x+2) x2 dx √4-x²

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

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Q: So(VE + vZ)° dx = f° xdx - (Vã + vZ)dx • f;(Vã + v2)dx 6. So x(x² + 1)dx = - S x*dx + f, xdx 7. S'…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 15) 4S(5x)] = x² , then f'(x) = ? %3D dx

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Q: A. Evaluate Inx dx. 2x B. Evaluate [(7x-10)dy dx. 0 x?

A: Note: Since you have posted multiple questions. We will solve the first question for you. If you…

Q: Find the value of the derivative. dy if y =7- 4x2 dx |x= - 2 dy (Simplify your answer.) %3D dx |x= -…

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Q: dæ4 evaluated at x = -1 dx evaluated at x = –1 dx? evaluated at x = -1 dx3 dªx4 evaluated at x = -1…

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Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

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Q: Q1) Find 2/3 dx a) Jas x*/9x² – 1 V2/3

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: .5 If f(x)dx 4 and | f(x)dx =7, then f(x)dx = %3D

A: Answer is below

Q: 4. Compute the following: (a) e dx -1 d (Ъ) dx f'(x) dx a

A: 4.(a) The objective is to find the value of ∫-11edx

Q: L, f(x)dx + [° f(x)dx = 5. Si f(x)dx – Sº f(x)dx = 4.

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Q: 18) fvī dx 19) f se'de 3e dx 20) (3x - V5x + 2) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the second derivative of the function. x4 + 6 y = x2 a²y 36 O A. = 2 - dx2 d²y 36 OB. = 2+ 4 X…

A: We have to find the second derivative of the function: y=x4+6x2 Rewriting the function,…

Q: d/dx(F(x^3))=d/dx(∫17 to x^3 e^−t2 dt)=

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Q: Find the value of the derivative. dy if y = 3 - 7x2 dx |x = - 3 dy (Simplify your answer.) %3D dx |x…

A: y=3-7x2dydx=0-14x       =-14x

Q: '5 If f(x) dx = 8 and f(x) dx = 5.3, find f(x) dx. If f(x) dx = 31 and g(x) dx = 14, find [4f(x) +…

A: 1. ∫17f(x)dx=8 and ∫57f(x)dx=5.32.∫07f(x)dx=31 and ∫07g(x)dx=14

Q: Sx² cos (x3 + 3) Van (x3• 3) dx + 3) Vsin (x3+ 3) dx 1)

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Q: dy when x=Ve is dx

A: