Chapter 6: Q. 7 (page 573)

Write down definite integrals to express the given geometric quantities :
The centroid $(\bar{x}, \bar{y})$ of the region between the graph of an integrable function $f$ and the x-axis on an interval $[a, b]$

Short Answer

Expert verified

$(\bar{x}, \bar{y}) = (\frac{\int_{a}^{b} x . f (x) d x}{\int_{a}^{b} f (x) d x}, \frac{\frac{1}{2} \int_{a}^{b} {(f (x))}^{2} d x}{\int_{a}^{b} f (x) d x})$

Step by step solution

Given Information :

Given that to assume that $f (x)$ is continuous and differentiable, with a continuous derivative.

Definite integral formula centroid of a region under a curve :

The centroid $(\bar{x}, \bar{y})$ of the region between the graph of $f (x)$ and the x-axis on the interval $[a, b]$ is

(\bar{x}, \bar{y}) = (\frac{\int_{a}^{b} x . f (x) d x}{\int_{a}^{b} f (x) d x}, \frac{\frac{1}{2} \int_{a}^{b} {(f (x))}^{2} d x}{\int_{a}^{b} f (x) d x})

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Write down definite integrals to express the given geometric quantities :
The centroid $(\bar{x}, \bar{y})$ of the region between the graph of an integrable function $f$ and the x-axis on an interval $[a, b]$

Short Answer

Step by step solution

Given Information :

Definite integral formula centroid of a region under a curve :

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Write down definite integrals to express the given geometric quantities :The centroid x¯,y¯of the region between the graph of an integrable function fand the x-axis on an interval a,b

Short Answer

Step by step solution

Given Information :

Definite integral formula centroid of a region under a curve :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Write down definite integrals to express the given geometric quantities :
The centroid $(\bar{x}, \bar{y})$ of the region between the graph of an integrable function $f$ and the x-axis on an interval $[a, b]$