If t is in "minutes," g(t) is in "gallons/foot," and v(t) is in "feet/minute," then the integral from a to b of g(t)v(t)dt is in what units?

Q: find the integral of F(x) = x6(x7-8)4 dx

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Q: If f(x)is the slope of a trail at a distance of x miles from the start of the trail, what does the…

A: Given∫35f(x)dxAnd we know that the total change theorem :∫35f(x)dx=F(5) - F(3)  ---{1}

Q: Give a geometric argument that explains why the integrals have equal values.

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Q: In evaluating / (2x – 3) Vx– 2 dr by substitution, if 4 =x - 2 then what will be the resulting…

A: Given : Indefinite integral ∫2x-3x-2 dx   To find : Resulting indefinite integral by substituting…

Q: do a double integral where x ranges from 0 to 1/2 and y ranges from 1/4 to 1/2

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Q: Use the properties to evaluate the integrals. 1. S; (1 + ) dx

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Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Evaluate the integral, if it exists.    ∫0T (x4 - 8x  +7) dx

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Q: The integral 9x? – x3 – 18x dx MUST be -1 evaluated by breaking it up into a sum of three integrals:

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Q: Evaluate the integral of (x^(3))*(e^(x^2))*dx

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Q: If you are asked to find the indefinite integral of f(x) = x ln(x), and you are told to integrate by…

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Q: Take the integral from 0 to 2 of (x/x2+4x+8)dx

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Q: If - 1 | f(2)dr = | f(x)dæ + / f(=)dr - /. f(æ)dx, what are the bounds of integration for the first…

A: I have used the properties of integration

Q: dx (1 – x3

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Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: Use substitution to find the indefinite integral

A: Given, ∫2+lnxx dx

Q: By-1 dy 2y+1

A: We have to solve given indefinite integral.

Q: Evaluate the integral. (Use C for the constant X - 7 dx x2 - 18x + 82

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Q: What is the integral of ((x^2)*e^(3x))dx from 0 to 1?

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Q: Evaluate the integrals ∫ ln x/x4 dx

A: The given integral is, I=∫lnxx4dx Substitute, lnx=t ⇒1xdx=dtx=etx3=e3t Therefore, the integral…

Q: [x² (-2 + x² )* dx

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Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A: We have to find the integral

Q: x²+2x+1 dx (x+2)(x−1)²

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Q: Evaluate the integrals ∫ ln x/x3 dx

A: Evaluate the integrals  ∫lnxx3dx

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫x dx/√x - 2

A: Given Integral is., I=∫xx-2dx

Q: sih (x) dx 6+x2

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Q: Find formulas for the functions represented by the integrals.

A: Find formula for the function represented by the given integral: ∫1x2 t dt

Q: Find the integral by using the integral table on the inside bac dx x(x + 5) + C

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Q: dx (x2 + 1)(x2 — 2х + 1)

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Q: What must be the value of C (constant of x² - 4 -dx so that the x +2 integration) to the integral of…

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Q: Evaluate the integrals. ∫x7√(x4 + 1) dx

A: The given integral is ∫x7x4+1dx.

Q: 17. Find the integral of ((x^4)/((x^2)+7))dx

A: Given: Let I=∫x4x2+7 dx To Find: To evaluate the given integration

Q: Evaluate the integrals ∫ ln x/x2 dx

A: Evaluate the integral ∫lnxx2dx.

Q: Use the table of integrals at the back of the text to evaluate the integrals ∫dx/x√x - 3

A: To evaluate the integral: ∫1xx-3dx. Let substitute u=x-3 dudx=12x-3dx=2x-3du Substituting the value,…

Q: In(sin x) d.x 2

A: We need to find whether given integral is proper of improper.

Q: ∞ Soo 8 2 "dx -7X e

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Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: Find the indefinite integral. 7x + 4e5x dæ ebx + 2e6x Integral = + C

A: Solve the integration .

Q: I need help solving the integral of the problem below.    ∫(√x+∛x)dx

A: Given integral can be written as

Q: the integral , dx is equal to: -2 x2+4x+5 4 2 the above the above

A: We will find the solution of the integral.

Q: If g(1)=−5, g(5)=9, and ∫from 1 to 5 g(x)dx=−8, evaluate the integral ∫from 1 to 5 xg′(x)dx.

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Q: What is the integral of 1/(x*sqrt(ln(x))) dx from 1 to e^2?

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Q: Evaluate the integrals in ∫e1/x/x2 dx

A: Our Aim is to evaluate the integral given below:-I=∫e1/xx2dx -(i)

Q: If V (t) is the amount of oil in a barrel being filled at time t, what physical quantity is…

A: Let's find.

Q: x6 dx V x14 - 3

A: ∫x6  dxx14-3 On simplification, we get ∫x6  dxx14-3=∫x6  dxx72-32 Now put, x7=t⇒7x6=dtdx⇒x6  dx=dt7…

Q: x4 – x³ – x – 1 dæ - x3 – x² -

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Q: ∫y + 3/(3-2)^2/3 dy

A: ∫ y+33-223dySimplify: =∫ y+3dyApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdx=∫ ydy+∫ 3dy=y22+3yAdd a…

Q: 3+ In(2x) dx 00 X-1 1

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Q: 5. fx³√√4 - 2x² dx

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