BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 5, Problem 8RE

(a)

To determine

The value of the integral function 01ddx(earctanx)dx.

Expert Solution

Answer to Problem 8RE

The value of the integral function is eπ41_

Explanation of Solution

Given information:

The integral function is 01ddx(earctanx)dx.

The region lies between x=0 and x=1.

Calculation:

Show the integral function as follows:

01ddx(earctanx)dx (1)

Apply the Fundamental Theorem of Calculus as follows:

F(x)=abG(x)dx

The expression to find the integral value by using Fundamental theorem of calculus as shown below.

01ddx(earctanx)dx=01ddx(earctanx)dx=(earctanx)01=(earctan1)(earctan0)=eπ4e0

01ddx(earctanx)dx=eπ41

Therefore, the value of the integral function is eπ41_.

(b)

To determine

The value of the integral function ddx01(earctanx)dx.

Expert Solution

Answer to Problem 8RE

The value of the integral function is 0.

Explanation of Solution

Given information:

The function as ddx01(earctanx)dx.

The region lies between x=0 and x=1.

Calculation:

Show the integral function as follows:

ddx01(earctanx)dx (2)

Use integral calculator to calculate the value as follows:

ddx01(earctanx)dx=ddx(1.591)=0

Therefore, the integral value of the function is 0. Since the definite integral is constant.

(c)

To determine

The value of the integral function ddx0xddx(earctant)dt.

Expert Solution

Answer to Problem 8RE

The value of the integral function is earctanx_.

Explanation of Solution

Given information:

The integral function is ddx0xddx(earctant)dt.

Calculation:

Show the integral function as follows:

ddx0xddx(earctant)dt (3)

The expression to find the integral value by using Fundamental theorem of calculus as shown below.

ddx0x(earctant)dt=earctanx

Therefore, the value of the integral function is earctanx_.

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