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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 5.4, Problem 4E

(a)

To determine

The value of

Expert Solution

The value of

The value of

**Given information:**

The equation is

The graph is given for the integral function

**Calculation:**

Show the integral function as below.

Here, *f* from *a* to *x* and *t*.

Determine

Substitute 0 for *x* in Equation (1).

Therefore, the

Determine

Refer the graph.

The curve is symmetrical about the point (3, 0). Hence, the area between the points 0 to 3 and 3 to 6 are equal with alternative sign.

Therefore, the function

(b)

To determine

The value of

Expert Solution

The value of

The value of

The value of

The value of

The value of

**Given information:**

The equation is

The graph is given for the integral function

**Calculation:**

Draw the graph for calculation of

Determine

Substitute 1 for *x* in Equation (1).

Refer Figure (1).

Area of shaded rectangle is the function of *t* with limits 0 to 1.

Modify Equation (2).

Add 80% of unit square.

Substitute 1 for *b,* 2 for *h*.

Therefore,

Draw the graph for calculation of

Determine

Substitute 2 for *x* in Equation (1).

Refer Figure (2).

Area of shaded rectangle is the function of *t* with limits 1 to 2.

Substitute 2.8 for *bh* for

Add 90% of unit square.

Substitute 1 for *b* and 1 for *h*.

Therefore,

Draw the graph for calculation of

Determine

Substitute 3 for *x* in Equation (1).

Refer Figure 3.

Area of shaded triangle is the function of *t* with limits 2 to 3.

Substitute 4.7 for *bh* for

Substitute 1 for *b* and 1.2 for *h*.

Therefore,

Draw the graph for calculation of

Determine

Substitute 4 for *x* in Equation (1).

Refer Figure 4.

Area of shaded triangle is the function of *t* with limits 3 to 4.

Substitute 5.3 for

Substitute 1 for *b* and 1 for *h*.

Therefore,

Draw the graph for calculation of

Determine

Substitute 5 for *x* in Equation (1).

Refer to Figure 5.

Area of shaded portion is the function of *t* with limits 4 to 5.

Substitute 4.7 for *bh* for

Subtract 90% of third unit square.

Substitute 1 for, 1 for *h*.

(c)

To determine

The interval when *g* is increasing.

Expert Solution

The function *g* is increasing at the interval

**Given information:**

The equation is

The graph is given for the integral function

**Calculation:**

Refer to Part (a).

The value of *g* is increasing from the interval 0 to 3.

Therefore, the function *g* is increasing at the interval

(d)

To determine

The location of maximum value of *g.*

Expert Solution

The maximum value of *g* lies at

**Given information:**

The equation is

The graph is given for the integral function

**Calculation:**

Refer part (a) calculation

Maximum value of *g* lies at

Therefore, the maximum value of *g* lies at

(e)

To determine

**To Sketch**: The rough graph of *g*.

Expert Solution

Plot the graph for function *f* using the calculated values of 0, 2.8, 4.7, 5.3 and 4.7 for the functions

Show the graph for function *f* as in Figure 6.

(f)

To determine

**To Sketch**: The graph

Expert Solution

Show the graph for function

Draw the graph