Q. 1 Give precise mathematical defini... [FREE SOLUTION]

Chapter 4: Q. 1 (page 402)

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.
a Riemann sum for a function $f$ on an interval $[a, b]$ , including the definitions of $螖 x, x_{k}$ , and $x_{k}^{*}$

Short Answer

Expert verified

Ans: $螖 x = \frac{b - a}{n}, x_{k} = a + k 螖 x$

Step by step solution

Step 1. Given information:

The Riemann sum for a function $f$ on an interval $[a, b]$ , including the definitions of $螖 x, x_{k}$ , and $x_{k}^{*}$

Step 2. Defining with a graph or algebraic example:

Generally, the Riemann sum approximates the area under the curve.

Consider the function $f$ is defined over an interval $[a, b]$ . The interval is divided into

n number of subintervals with equal width $螖 x .$ .

Here, $螖 x = \frac{b - a}{n}$ .

Here, $x_{k}$ is the $k^{t h}$ end point of the subintervals. $x_{k} = a + k 螖 x$

Then the Riemann sum

${鈭�}_{a}^{b} f (x) d x = {鈭�}_{k = 1}^{n} f ({x_{k}}^{*}) 螖 x$

Here, $螖 x = \frac{b - a}{n}, x_{k} = a + k 螖 x$ .

$x_{k} {}^{*}{鈫�}$ is the any sample point in the sub interval

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Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.
a Riemann sum for a function $f$ on an interval $[a, b]$ , including the definitions of $螖 x, x_{k}$ , and $x_{k}^{*}$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Defining with a graph or algebraic example:

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91影视

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.a Riemann sum for a function f on an interval [a,b], including the definitions of 螖x,xk, and xk*

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Defining with a graph or algebraic example:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Decision Maths

Discrete Mathematics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.
a Riemann sum for a function $f$ on an interval $[a, b]$ , including the definitions of $螖 x, x_{k}$ , and $x_{k}^{*}$