Q. 7 Write down definite integrals to... [FREE SOLUTION]

Chapter 6: Q. 7 (page 573)

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

Short Answer

Expert verified

$(\overset{炉}{x}, \overset{炉}{y}) = (\frac{{鈭�}_{a}^{b} x . f (x) d x}{{鈭�}_{a}^{b} f (x) d x}, \frac{\frac{1}{2} {鈭�}_{a}^{b} {(f (x))}^{2} d x}{{鈭�}_{a}^{b} f (x) d x})$

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

(\overset{炉}{x}, \overset{炉}{y}) = (\frac{{鈭�}_{a}^{b} x . f (x) d x}{{鈭�}_{a}^{b} f (x) d x}, \frac{\frac{1}{2} {鈭�}_{a}^{b} {(f (x))}^{2} d x}{{鈭�}_{a}^{b} f (x) d x})

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Write down definite integrals to express the given geometric quantities :
The centroid $(\overset{炉}{x}, \overset{炉}{y})$ 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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91影视

Write down definite integrals to express the given geometric quantities :The centroid x炉,y炉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

Logic and Functions

Mechanics Maths

Pure Maths

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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