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The acceleration function (in m / s2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. The acceleration function (in m / s<sup>2</sup>) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. A) B) C) D) E)


A) The acceleration function (in m / s<sup>2</sup>) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. A) B) C) D) E)
B) The acceleration function (in m / s<sup>2</sup>) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. A) B) C) D) E)
C) The acceleration function (in m / s<sup>2</sup>) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. A) B) C) D) E)
D) The acceleration function (in m / s<sup>2</sup>) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. A) B) C) D) E)
E) The acceleration function (in m / s<sup>2</sup>) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval. A) B) C) D) E)

F) B) and E)
G) A) and E)

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Find the integral using the indicated substitution. Find the integral using the indicated substitution. , A) B) C) D) , Find the integral using the indicated substitution. , A) B) C) D)


A) Find the integral using the indicated substitution. , A) B) C) D)
B) Find the integral using the indicated substitution. , A) B) C) D)
C) Find the integral using the indicated substitution. , A) B) C) D)
D) Find the integral using the indicated substitution. , A) B) C) D)

E) None of the above
F) A) and B)

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Let Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . . a.Use Part 1 of the Fundamental Theorem of Calculus to find Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . is differentiable on (a, b), and Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . where F is any antiderivative of f, that is, Let . a.Use Part 1 of the Fundamental Theorem of Calculus to find . b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for F(x). c.Differentiate the expression for F(x) found in part (b).The Fundamental Theorem of Calculus, Part 1 If f is continuous on [a, b], then the function F defined by is differentiable on (a, b), and The Fundamental Theorem of Calculus, Part 2 If f is continuous on [a, b], then where F is any antiderivative of f, that is, . .

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The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. A) B) C) D)


A) The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. A) B) C) D)
B) The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. A) B) C) D)
C) The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. A) B) C) D)
D) The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression as a definite integral on [a, b]. A) B) C) D)

E) A) and C)
F) All of the above

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The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval. The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval. A) 100 m B) 72 m C) 36 m D) 64 m E) 68 m


A) 100 m
B) 72 m
C) 36 m
D) 64 m
E) 68 m

F) A) and E)
G) A) and D)

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Find the indefinite integral. Find the indefinite integral.

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Determine a region whose area is equal to Determine a region whose area is equal to . A) B) C) D) E) .


A) Determine a region whose area is equal to . A) B) C) D) E)
B) Determine a region whose area is equal to . A) B) C) D) E)
C) Determine a region whose area is equal to . A) B) C) D) E)
D) Determine a region whose area is equal to . A) B) C) D) E)
E) Determine a region whose area is equal to . A) B) C) D) E)

F) B) and D)
G) C) and D)

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Evaluate the integral. Evaluate the integral. A) 1.000 B) -0.500 C) 0.250 D) -1.000 E)


A) 1.000
B) -0.500
C) 0.250
D) -1.000
E) Evaluate the integral. A) 1.000 B) -0.500 C) 0.250 D) -1.000 E)

F) A) and D)
G) A) and C)

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Evaluate the integral. Evaluate the integral. A) B) C) D) E)


A) Evaluate the integral. A) B) C) D) E)
B) Evaluate the integral. A) B) C) D) E)
C) Evaluate the integral. A) B) C) D) E)
D) Evaluate the integral. A) B) C) D) E)
E) Evaluate the integral. A) B) C) D) E)

F) C) and D)
G) A) and C)

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Evaluate the indefinite integral. Evaluate the indefinite integral. A) B) C) D) E)


A) Evaluate the indefinite integral. A) B) C) D) E)
B) Evaluate the indefinite integral. A) B) C) D) E)
C) Evaluate the indefinite integral. A) B) C) D) E)
D) Evaluate the indefinite integral. A) B) C) D) E)
E) Evaluate the indefinite integral. A) B) C) D) E) Evaluate the indefinite integral. A) B) C) D) E)

F) B) and C)
G) A) and E)

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Evaluate the indefinite integral. Evaluate the indefinite integral.

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The table gives the values of a function obtained from an experiment. Use the values to estimate The table gives the values of a function obtained from an experiment. Use the values to estimate using three equal subintervals with left endpoints. w 0 1 2 3 4 5 6 f (w) 9.7 9.1 7.7 6.1 4.2 -6.6 -10.3 using three equal subintervals with left endpoints. w 0 1 2 3 4 5 6 f (w) 9.7 9.1 7.7 6.1 4.2 -6.6 -10.3

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Find a function f (x) such that Find a function f (x) such that for and some number a. for Find a function f (x) such that for and some number a. and some number a.

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Evaluate by interpreting it in terms of areas. Evaluate by interpreting it in terms of areas.

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Use the Midpoint Rule with Use the Midpoint Rule with to approximate the integral. Round the answer to 3 decimal places. to approximate the integral. Round the answer to 3 decimal places. Use the Midpoint Rule with to approximate the integral. Round the answer to 3 decimal places.

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