# The sum value of the function using computer algebra system.

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 5, Problem 6RE

(a)

To determine

## The sum value of the function using computer algebra system.

Expert Solution

The sum value of the function is 5,220.

### Explanation of Solution

Given information:

The function as 15(x+2x5)dx.

The region lies between x=1 and x=5.

The expression to find the sum value when the sample points at right endpoints are shown below:

15(x+2x5)dx=limni=1nf(xi)Δx (1)

Here, the height of sample at the right endpoint is f(xi) and the width is Δx.

Find the width (Δx) using the relation:

Δx=ban (2)

Here, the upper limit is b, the lower limit is a, and the number of rectangles is n.

Substitute 5 for b and 1 for a in Equation (2).

Δx=51n=4n

To find the value of xi using the relation:

xi=a+iΔx (3)

Substitute 1 for a and 4n for Δx in Equation (3).

xi=1+i4n=1+4in

Substitute (xi+2xi5) for f(xi) in Equation (1).

15(x+2x5)dx=limni=1n(xi+2xi5)Δx (4)

Substitute 4n for Δx and 1+4in for xi in Equation (4).

15(x+2x5)dx=limni=1n[(1+4in)+2(1+4in)5](4n)=(4n)[limni=1n(1+4in)+limni=1n2(1+4in)5]=CASlimn(1,305n4+3,126n3+2,080n2256n3)(4n)=4×limn(1,305+3,126n+2,080n2256n4)

15(x+2x5)dx=4×1,305=5,220

Therefore, the sum value of the function is 5,220.

(b)

To determine

### The value of the integral using the fundamental theorem.

Expert Solution

The value of the integral is 5,220.

### Explanation of Solution

Given information:

The function as 15(x+2x5)dx.

The region lies between x=1 and x=5.

The expression to find the value of the integral using the fundamental theorem is shown below:

15(x+2x5)dx=(12x2+26x6)15=(12×52+26×56)(12×12+26×16)=12.5+5,208.330.50.33=5,220

Therefore, the value of the integral using the fundamental theorem is 5,220.

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