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Chapter 4: Q.16 (page 352)

Suppose fis an integrable function [a,b]and kis a real number. Use pictures of Riemann sums to illustrate that the right sum for the function kf(x)on [a,b]is ktimes the value of the right sum (with the same n) for fon [a,b]. What happens as n鈫�鈭�? What does this exercise say about the definite integrals鈭�abf(x)dxand鈭�abkf(x)dx?

Short Answer

Expert verified

鈭�02x2dx

Step by step solution

01

Given information

Suppose is an integrable function and is a real number. Use pictures of Riemann sums to illustrate that the right sum for the function on is times the value of the right sum (with the same ) for on . What happens as ? What does this exercise say about the definite integralsand

02

Calculation

The given region is under the function and starts at and ends at , so the required definite integral is:

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Most popular questions from this chapter

Sum and constant-multiple rules: State the sum and constant-multiple rules for (a) derivatives and (b) limits.

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鈭�23x+1dx
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