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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 5.4, Problem 3E

(a)

To determine

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 integral function is

**Calculation:**

Show the integral function as below.

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

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

Therefore, the

Draw the graph for calculation of

Determine

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

Refer to Figure (1).

Modify Equation (2).

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

Therefore, the

Draw the graph for calculation of

Determine

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

Refer to figure 2.

The area of shaded triangle and rectangle is the function of *t* with limits 1 to 2.

Substitute

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

Therefore, the

Draw the graph for calculation of

Determine

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

Refer to Figure 3.

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

Substitute 5 for

Substitute 1 for *b* and 4 for *h*.

Therefore, the

Draw the graph for calculation of

Determine

Refer to Figure 4.

Area of shaded portion is the function of *t* with limits 5 to 6.

Substitute 2for

Therefore, the

(b)

To determine

The interval *g*.

Expert Solution

The function *g* is increasing at the interval

**Given information:**

The integral function is

**Calculation:**

Refer Part (a).

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

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

(c)

To determine

The maximum value of *g*.

Expert Solution

The maximum value of *g* is lies at

**Given information:**

The integral function is

**Calculation:**

Refer part (a) calculation

Maximum value of *g* lies at

Therefore, the maximum value of *g* lies at

(d)

To determine

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

Expert Solution

The graph for function *f* is shown in Figure 1.

Plot the graph for function *f* using the calculated values of 0, 2,5,7,3 for the functions

Draw the graph for function of *f* as in Figure (5).