Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: Find the antiderivative F of f(x)=4-3(1+x^2)^-1 that satisfies F(1)=-2.

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Q: Find the most general antiderivative of f(x) = -3x – 7xL7. Note: Any arbitrary constants used must…

A: Topic = Integration

Q: Hello! What is the solution to this question? Thank you for your help! Have a nice day :)

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Q: Suppose f= f(x) satisfies f(1) = 7 and f(1.002) 7.008. Estimate the value of at x = 1. dt %3D

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Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: If f(x)= integral subscript 2 superscript x fraction 1+t/1+t^2 dt, then what is f'(-3)?

A: f(x)=∫2x1+t1+t2dt, find f'(-3)

Q: Show that f(x) = 0(\x – #o|*) and g(x) f • g(x) = o(\x – xol*+i). o(lx – xo|2) imply -

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Q: 6 3 Consider the function f(x) x2 = 0. Let F(x) be the antiderivative of f(x) with F(1) = Then F(x)

A: We can find the antiderivative of the given function by using the following formula.

Q: Find all antiderivatives of function:  f (x) = e3x

A: Given- fx=e3x To Find- The antiderivative of the above expression.

Q: Suppose that f(x) is an antiderivative of f(x) = V1 + xt. Express JoV1 + x* dx in terms of F and…

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Q: Suppose that F(x) = –3x* is an antiderivative of f (x) and G(x) = 2x' is an antiderivative of g(x).…

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Q: 2 Consider the function f(x) - x7 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

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Q: Suppose that f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) = 3, and f" is continuous. Find the value of *…

A: Use the method for integration by parts to solve the integral.

Q: Find the particular antiderivative F(x) of f(x) = x6 1 that satisfies F(1) = 4. - %3D

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Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: The function f(x) = x + 1/x is O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1, 0) O…

A: Answer is written below

Q: Let f(x) x2 + 1 Enter an antiderivative of f(x)

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Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

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Q: Find the antiderivative F(x) of f(x)= 3√x that satisfies F(1)=2

A: The given function, f(x)=x3

Q: Find the most general antiderivative of the functions: 1)f(X)= 2secxtanx-3sinx 2)f(X)=…

A: (1) Given, f(x) = 2secxtanx-3sinx  ∫f(x)dx = ∫(2secxtanx-3sinx )dx               = ∫(2secxtanx)dx -…

Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

Q: Find an antiderivative of the function f(x)=1/x4.

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Q: Differentiate f(x) = f'(x) = 2 ax with respect to x. Assume that a and k are positive constants. k+x

A: To differentiate fx=ax2k+x with respect to x. Assume that a and k are positive constants.

Q: Suppose F is an antiderivative of f(x) = VT. If F(0) 1 then F(1) 4 %3D %3D is 3 A. –1, B. -, C. 0,…

A: Let f be a function . Suppose F is a function such that  F'(x) =f(x) then F is an antiderivative of…

Q: f(x) = 2x° –x + 5x f(x) = 3/x – 2x

A: We know ∫xn dx = xn+1n+1+C     n≠-1   where C is constant of integration.

Q: The function f(x) =x + 1/x is concave upward on none O (-1) O (0,) O (0,1) O (1,)

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Q: Let f(x) = V1+x. Estimate the change in f from x = 7 to x = 7.5 using linear approximation. %3D

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Q: Find the particular antiderivative F(x) of f(x) = x + that satisfies F(1) = 3. %3D

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Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

Q: Find the most general antiderivative of f(x) 2x-1+x.

A: Given,            f(x) = 2x2 - 1 + x-2

Q: If f(x) = 1-x* , then an antiderivative F(x) could be Inx| -x А. 6-x C. 5x 3x 5 Inx| – x* 1+x° В. D.…

A: f(x) = 1-x5xAntiderivative F(x) = ∫ 1-x5xdx∫ 1-x5xdx= ∫1x-x4dx= ∫1xdx - ∫x4dx= ln x - x55 +…

Q: The function f(x) = x + 1/x is 2p O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1,…

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Q: Suppose that f : R → [0, 0) is measurable. (positive) show that if f R then F=0 a.e

A: For the solution follow the next step.

Q: The antiderivative of f(x) is unique. True False

A: Thus, The antiderivative of function is not unique, but is unique up to a constant.

Q: Suppose f(1) = 0,f(3) = 1,f'(1) = 2 , and f'(3) = -3. Evaluate Sxf"(x) dx. %3D

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Q: Find the antiderivative F of f that satisfies the given conditions. SHOW WORK!!! 1. 4Vx + f(x) = ;…

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Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: Let f(x)= x3 + 2x1/2. Find F(x), where F(x) is the antiderivative of f(x) that passes through the…

A: Integrate

Q: 2 10 Consider the function ƒ(x) : x3 x7 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A: We have to integral the given function and find the constant of integration.

Q: 7 10 Consider the function f(x) - x2 x6 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A: Given that F(x) is the antiderivative of f(x) then F(x) = integration of f(x).

Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: Show that F(x) = (x + 1)*(x – 2)3 is an antiderivative of the function f(x) = (7x – 5)(x + 1)³(x –…

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Q: Suppose that the function f is continuous everywhere. Suppose that F is any antiderivative of f, and…

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Q: Find f(3,4) for f (x, y) = In(x + /x² + y²). %3D

A: Given:- f(x, y) =ln(x+√(x2+y2))  To find:- fx(x, y) at (3, 4)

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

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Q: Find constants c1 and c2 such that F(x) = c1xe -x + c2e -x is an antiderivative of f(x) = 3xe -x .

A: Given: Fx=C1xe-x+C2e-x  and fx=3xe-x

Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.