If dx - F(x) =f(x) and F(– 1) = F(2) = – 5, then f(x)dx = %3D

Q: f(x) dx = -4, f(x) dx = 6, g(x) dx = 8 - If g(x) dx b. c. 3f(x) dx d. dx x) - g(x)] dx g(x)] dx e.…

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Q: dy 3. + y = e3x dx

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Q: Example 2: Solve (y + x)dy + (x – y)dx = 0 .

A: The given differential equation is y+dy+x-ydx=0. Simplify as follows.…

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Q: 1 + e1x+10 + 4" +x – 5) dx + xA 4x-

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Q: d²y dy 6. 2+ 8y = e-3x dx 1. Solve dx²

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Q: 2- e dx 十e X X e dx 2.

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Q: f(x)dx = 2, 5 and 8 f(x)dx = -5, then, 8 f(x)dx = -3

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Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

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Q: Calculate dy. dx2 y = -6x2 + 7x dy dx2

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Q: Find the constants a and b that maximize the value of -x²) dx. (a, b) =

A: ∫ab(1-x2)dx

Q: 2. S (x * - x³ -3x) dx V4

A: Explanation of the answer is as follows

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Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

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Q: Calculate  d2y dx2 y =  −  5 x2  d2y dx2 =

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Q: (a) S - dx 1+e2x 4x (b). dx 1-x dx (c) S- dx x2+2x+10

A: Questions are solved.Here are its solution.

Q: · 8 Find f(x) dx = 5 (5 f(x) – 6) dx 8, and

A: Given ∫211f(x)dx=5∫25f(x)dx=6∫811f(x)dx=4

Q: Solve. d²y dy -(2x+1): +(x+1) y=(x² +x-1)e²* dx dx

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Q: dy 2x y3 – 4y dx II

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Q: 2y d³y dx3 (y + 3 dx) dy dx² + 2

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Q: What values of a and b maximize the value of (x-x²) dx.

A: Find your answer below

Q: Let ƒ(x) = x3 - 3x2 - 1, x>= 2. Find the value of dƒ -1/dx at the point x = -1 = ƒ(3).

A: We will need inverse function theorem. Statement of the theorem is:

Q: 3x -1 dx is equal to

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Q: 10. fS'(x)dx -4

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Q: 2. S (2x-5)dx x2-5x+3

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Q: 2 S (x² – 4| – |æ – 1)) dæ - 4| – |x – 1|) dx -2

A: Definite integration

Q: 8. S(x³ + 2x² +x – 5)e2* dx -

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Q: @[² (d) √x-x (x² + y²)³/2 dy dx.

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Q: Find the formula for df-1 /dx. f(x) = (1 – x)3 1 O A. 3x2/3 О В. 1-х1/3 Ос. -3(1- х)?

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Q: d -(f(x² + 3x)) dx

A: Derivative

Q: Find d2y/dx2 implicitly in terms of x and y. x2y − 3x = 8   d2y/dx2 =

A: Consider the given function, x2y-3x=8 use implicit differentiation method and differentiate with…

Q: In the function given. Evaluate the integrals.

A: ∫36-3gxdx=∫36-3dx·∫36gxdx Also, ∫36gxdx=1

Q: dx -3 +2x dt = 2 is

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Q: If f(x) dx = 3 and f(x) dx = 4 what is the value of %3D 5f(x) dx?

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Q: dx S- x4 - 1

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Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

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Q: 2 S. x*- 4x +4 dx (メ-2)(x4) |

A: Solution: Consider the given integral is: I = ∫x2-4x+4(x-2)(x2+4)dxI = ∫x-22(x-2)(x2+4)dxI =…

Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: How do you integrate: xe11x dx ?

A: Given integral

Q: -4 (1x|+x-2|) dx -1

A: To find: The integral ∫-14x-x-2dx. Concept used: The absolute function fx=x: fx=x,    x≥0-x, x<0…

Q: dx 1) S- x2-2x+1

A: As per the guidelines we can only solve one question post other question seperately. Formula used  ∫…

Q: Find the value of (x)) dx if f(x) dx=11 and f(x) dx=3.

A: here we have to find the integral vaule

Q: If ƒ x Inx dx = x² In x – S f(x)dx, what is the value of , 4f (x)dx?

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: x² +x-2 -dx can be resolved into (x2-1)(2x-x²)

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Q: -2 S.f(x)dx -4 a. b.5°2f1x) dx C.5f(x) dx

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Q: dy у+x3 + 3x2 - 2х dx %3

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Q: 2 dx X + X - e メ-

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Q: find dy/dx.x^-4/4 - x^-3/3 +x^-2/2 -x^-1 +e

A: We have given,

Q: calculate d2y/dx2 when y=e-(x-3)-x

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Q: e6x (a) : dx 4+ e6x (b) /: dx 4+ e6x 3 (с) dx V4– x2

A: Since you have posted multiple questions i can answer first three as per our company guidelines…