Chapter 4: Q. 42 (page 340)

In Exercises 39–44, write out the sigma notation for the Riemann sum described in such a way that the only letter which appears in the general term of the sum is k. Don’t calculate the value of the sum; just write it down in sigma notation.
$f (x) = \ln (x), [a, b] = [2, 5], l e f t s u m, n = 100$

Short Answer

Expert verified

The left sum is $= 0.03 \sum_{k = 1}^{100} \ln (2 + 0.03 (k - 1))$

Step by step solution

Step 1. Given Information

The given function is $f (x) = \ln (x), [a, b] = [2, 5], l e f t s u m, n = 100$

Step 2. Finding ∆x and xk

$∆ x = \frac{b - a}{n} = \frac{5 - 2}{100} = \frac{3}{100} = 0.03$

$x_{k} = a + k ∆ x = 2 + 0.03 k x_{k - 1} = a + (k - 1) ∆ x = 2 + 0.03 (k - 1)$

Step 3. Finding Reimann Sum

We have $f (x) = \ln (x)$ then $f (x_{k - 1}) = \ln (x_{k - 1})$

Now, $\sum_{k = 1}^{100} f (x_{k - 1}) ∆ x = \sum_{k = 1}^{100} \ln (2 + 0.03 (k - 1)) (0.03) = 0.03 \sum_{k = 1}^{100} \ln (2 + 0.03 (k - 1))$

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding ∆x and xk

Step 3. Finding Reimann Sum

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In Exercises 39–44, write out the sigma notation for the Riemann sum described in such a way that the only letter which appears in the general term of the sum is k. Don’t calculate the value of the sum; just write it down in sigma notation.fx=lnx,a,b=2,5,leftsum,n=100

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding ∆x and xk

Step 3. Finding Reimann Sum

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Decision Maths

Discrete Mathematics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.