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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 5.4, Problem 2E

(a)

To determine

The value of

Expert Solution

The value of

The value of

The value of

The value of

The value of

The value of

The value of

**Given information:**

The equation is

**Calculation:**

Show the integral function as below:

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

Determine

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

Therefore,

Draw the graph for the calculation of

Determine

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

Refer to Figure (1).

The area of the shaded triangle is the function of *t* with limits 0 to 1.

Modify Equation (2).

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

Therefore,

Draw the graph for the calculation of

Determine

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

Refer to Figure (2).

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

Substitute

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

Therefore,

Draw the graph for the calculation of

Determine

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

Refer to Figure 3.

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

Substitute

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

Therefore,

Draw the graph for the calculation of

Determine

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

Refer to Figure 4.

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

Substitute

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

Therefore,

Draw the graph for the calculation of

Determine

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

Refer to Figure 5.

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

Substitute

Substitute 1 for

Therefore, the

Draw the graph for the calculation of

Determine

Substitute 6 for *x* in Equation (1).

Refer to Figure 6.

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

Substitute 1.5 for

Substitute 1 for

Therefore,

(b)

To determine

The value of

Expert Solution

The value of

**Given information:**

The equation is

**Calculation:**

Draw the graph for the calculation of

Determine

Substitute 7 for *x* in Equation (1).

Refer to Figure 7.

The area of the shaded portion is the function of *t* with limits 6 to 7; it is bounded by a curved shape. Hence, take the approximate value from the graph

Take the approximate area of the shaded portion as 2.2

Substitute 4 for

Therefore,

(c)

To determine

The maximum and minimum value of *g*.

Expert Solution

The minimum value of *g* lies at

**Given information:**

The equation is

**Calculation:**

From the calculation in Part (A),

The minimum value of function of *g* is

The maximum value of function of *g* is 6.2 at

Therefore, the minimum value of *g* lies at

(d)

To determine

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

Expert Solution

Plot the graph for function *f* using the calculated values of 0,

Draw the graph for the function of *f* as in Figure (8).