Webwork Section 1.3: fundamental theorem of calculus PDF

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Webwork ch 1 problems 1-20, section 1.3: fundamental theorem of calculus...

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Sarah Galvan MAT 1224 007 Fall 2021 Assignment HW Section 1.3 The Fundamental Theorem of Calculus due 08/30/2021 at 11:59pm CDT Problem 8. (1 point)

Problem 1. (1 point) Use the Fundamental Theorem of Calculus to find the derivative. If g(x) =

Z x

If f (x) = then f ′ (x) =

g′ (x) =

Problem 9. (1 point) If f (x) =

Problem 2. (1 point) Use the Fundamental Theorem of Calculus to find the derivative. If g(x) =

Z x

f ′ (x) =

If f (x) =

g′ (x) =

t 2 dt then

−2

Z x4

t 5 dt

x

then f ′ (x) =

Problem 3. (1 point) Use the Fundamental Theorem of Calculus to find the derivative. Z √x

Z x3

Problem 10. (1 point)

2

e−t dt then,

11

If g(x) =

t 3 dt

x

3 dt then, t3 − 5

−7

Z 6

Problem 11. (1 point) If f (x) =

tdt then,

Z x

(t 3 + 6t 2 + 5)dt

0

6

g′ (x) = Problem 4. (1 point) Use the Fundamental Theorem of Calculus to find the derivative.

Problem 12. (1 point) Part1.

Z d sin x p

1 − t 2 dt = dx 6 Problem 5. (1 point) Use the Fundamental Theorem of Calculus to find the derivative.

Find the most general antiderivative by evaluating the following indefinite integral: Z   x2 − 11x dx =

Z x d e  2 ln u du = dx 10 Problem 6.Z(1 point) x

NOTE: The general antiderivative should contain an arbitrary constant.

t 3 dt. Evaluate the following.

Let f (x) =

−1

Part 2.

f ′ (x) = f ′ (4) = Problem 7. (1 point) If f (x) =

Z 19

Evaluate the given definite integral. Z −1 

4

t dt then

−4

x

f ′ (x) = 1

 x2 − 11x dx =

Problem 13. (1 point)

Problem 15. (1 point)

Part1.

Part1.

Find the most general antiderivative by evaluating the following indefinite integral:

Find the most general antiderivative by evaluating the following indefinite integral:

Z    x2 − 1 9 − x2 dx =

Z 

NOTE: The general antiderivative should contain an arbitrary constant.

NOTE: The general antiderivative should contain an arbitrary constant.

Part 2.

Part 2.

Evaluate the given definite integral.

Evaluate the given definite integral.  Z 2 −5 − dt = 2t 1

Z −1 

x2 − 1

−4

−

  9 − x2 dx =

−5 2t



dt =

Problem 14. (1 point)

Problem 16. (1 point)

Part1.

Part1.

Find the most general antiderivative by evaluating the following indefinite integral:

Find the most general antiderivative by evaluating the following indefinite integral:

Z 

Z

1 12t 2

+ 6t

2



dt =

sec2 (θ)dθ =

NOTE: The general antiderivative should contain an arbitrary constant.

NOTE: type ’theta’ for the variable θ NOTE: The general antiderivative should contain an arbitrary constant.

Part 2.

Part 2.

Evaluate the given definite integral.

Evaluate the given definite integral.

Z 16 

Z 7π 4

9

 1 12t 2 + 6t 2 dt =

2π

2

sec2 (θ)dθ =

Problem 18. (1 point) Evaluate the definite integral

Problem 17. (1 point)

Z 8

Part1.

4

Find the most general antiderivative by evaluating the following indefinite integral: Z

Problem 19. (1 point) Evaluate the definite integral Z 5

7 dx = 1 + x2

2

Z 7 2 2x + 2 4

Part 2.

√

3 3

3 3

√ dx x

Problem 21. (1 point) Evaluate the definite integral

Evaluate the given definite integral. √

(12x2 − 4x + 2)dx

Problem 20. (1 point) Evaluate the definite integral

NOTE: The general antiderivative should contain an arbitrary constant.

Z −

(2x + 6)dx

Z π

7 dx = 1 + x2

0

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2 sin(x)dx...