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

Short Answer

Expert verified

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

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 $(\bar{x}, \bar{y})$ 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 $(\bar{x}, \bar{y})$ 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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Write down definite integrals to express the given geometric quantities :The centroid x¯,y¯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

Discrete Mathematics

Mechanics Maths

Calculus

Applied Mathematics

Geometry

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