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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

(a) Write 1 5 ( x + 2 x 5 )   d x as a limit of Riemann sums, taking the sample points to be right endpoints. Use a computer algebra system to evaluate the sum and to compute the limit.

(b) Use the Fundamental Theorem to check your answer to part (a).

To determine

a)

To write:

15(x+2x5)dx as limit of Riemann sum

Explanation

1) Concept:

i) Definition of Riemann sum:

abfxdx=limni=1nfxi* x

Where,

x= b-an  and  xi=a+i x

ii) The Fundamental Theorem of Calculus-Suppose f is continuous on [a, b]  then

abfxdx=Fb-F(a), F is an antiderivative of  f i.e F'=f

iii) Power rule of Integration:

xndx=xn+1n+1+C

2) Given:

15(x+2x5)dx

3) Calculation:

We have,

15(x+2x5)dx

Here a=1, b=5

x= b-an

= 5-1n

x=4n

xi=a+i x

=1+i·4n

To determine

b)

To check:

15(x+2x5)dx=5220

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