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2. [-73 Points]

DETAILS

SCALC8 4.3.005.

Sketch the area represented by g(x).

g(x) =

t4 dt

у

t

1

х

y

t

1

Then find g'(x) in two of the following ways.

(a) by using Part 1 of the Fundamental Theorem

g'(x) =

(b) by evaluating the integral using Part 2 and then differentiating

g'(x) =

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1. [-/8 Points]

DETAILS

SCALC8 4.3.003.

MY NOTES

ASK YOUR

Let g(x) =

ES

f(t) dt, where f is the function whose graph is shown.

y

f

4

t

4

20

(a) Evaluate g(0), g(4), g(8), g(12), and g(24).

g(0) =

g(4) =

g(8) =

9(12) =

g(24) =

(b) On what interval is g increasing? (Enter your answer using interval notation.)

(c) Where does g have a maximum value?

X =

(d) Sketch a rough graph of g.

у

у

16

g(x)

X

4

16

g(x)

4

у

у

16

4

g(x)

16

X

4

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2. [-/3 Points]

DETAILS

CAL

45.00

MY NOTES

ASK YOUR

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3. [-/1 Points]

DETAILS

SCALC8 4.3.007.

MY NC

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

g(x)

– [* VR + ede

g'(x) =

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4. [-/1 Points]

DETAILS

SCALC8 4.3.011.

MY NC

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

X

F(x) =

– ſºva

V 8 + sec(3t) dt

Hint:

0

V 8 + sec(3t) dt = –

-6

V8 + sec(3t) d

dt

F'(x) =

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5. [-/1 Points]

DETAILS

SCALC8 4.3.019.

MY NC

Evaluate the integral.

La

(x2 + 2x – 4) dx

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6. [-/1 Points]

DETAILS

SCALC8 4.3.021.

MY NC

Evaluate the integral.

5 * * 3 – 2 2 + şe) de

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7. [-/1 Points]

DETAILS

SCALC8 4.3.023.

MY NC

Evaluate the integral.

√x ax

10:14

..Il LTE

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7. [-/1 Points]

DETAILS

SCALC8 4.3.023.

MY NC

Evaluate the integral.

9

$

√x dx

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8. (-/1 Points]

DETAILS

SCALC8 4.3.027.

MY NC

Evaluate the integral.

“1

to

(u + 2)(u – 3) du

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9. [-/1 Points]

DETAILS

SCALC8 4.3.029.

MY NO

Evaluate the integral.

79 6 + x2

dx

√x

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10. [-/1 Points]

DETAILS

SCALC8 4.3.037.

MY NO

Use a graph to give a rough estimate of the area of the region that lies beneath the given cur

y = 2 sin(x), 0

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