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 6RE

(a)

To determine

The sum value of the function using computer algebra system.

Expert Solution

Answer to Problem 6RE

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

Answer to Problem 6RE

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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