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Q. 6

Question

Explain geometrically what the definition of the definite integral as a limit of Riemann sums represents. Include a labeled picture of a Riemann sum (for a particular n) that illustrates the roles of n, x, ∆x, xk* and f(x*k). What happens in the picture as n → ∞?

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m

1Step 1. Given information

a

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Other exercises in this chapter

Q. 4
Explain why it makes sense that every Riemann sum for a continuous function f on an interval [a, b] approaches the same number as the number n of
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Q. 5
Fill in the blanks: The definite integral of an integrable function f from x=a to x=b is defined to bewhere ∆x=_____, xk=________
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Q. 6
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Q. 7
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