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 graphs of two integrable functions $f (x)$ and $g (x)$ on an interval $[a, b]$ .

Short Answer

Expert verified

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

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 between two curves :

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

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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 graphs of two integrable functions $f (x)$ and $g (x)$ on an interval $[a, b]$ .

Short Answer

Step by step solution

Given Information :

Definite integral formula centroid of a region between two curves :

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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 graphs of two integrable functions fxand gxon an intervala,b.

Short Answer

Step by step solution

Given Information :

Definite integral formula centroid of a region between two curves :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Applied Mathematics

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 graphs of two integrable functions $f (x)$ and $g (x)$ on an interval $[a, b]$ .