A region in the plane is bounded by the graph of y=1/x, the x-axis, the line x=m and the line x=3m, m>0. the area of this region:

Ais independent of m
Bincreases as m increases
Cdecreases as m increases
Ddecreases for all m<1/3
Eincreases for all m<1/3

The area bounded by the graph of \(\rm y=\frac{1}{x}\) , the x-axis, the line x=m and x=3m is log3, which is independent of m ie. option (a) is true.

It is given that the region in the plane is bounded by the graph of \(\rm y=\frac{1}{x}\) ,

the x-axis, the line x = m and x = 2m where m >0.

It is required to find which of the following statement is true.

What is the area under the curve?

It is defined as the area bounded by the curves it can be calculated using definite integrals between the two limits ie. lower and higher limits.

We have curves such that:

\(\rm y=\frac{1}{x}\) , x-axis , the lines x = m, and x =2m

The area under the curve = (integration of the given curve between m to

2m)

\(\rm A= \int_{m}^{3m}\frac{1}{x}dx\\\\\rm A = [logx]_{m}^{3m}\\\\\rm A = log3m-logm\\\\\rm A = log\frac{3m}{m} \\\\\rm A = log3\)∵ \(\rm [{\int \frac{1}{x} dx = logx }]\) and \(\rm[logx-logy=log\frac{x}{y} ]\)

Thus, the area bounded by the graph of \(\rm y=\frac{1}{x}\) , the x-axis, the line x=m and x=3m is log3, which is independent of m ie. option (a) is true.

Learn more about the area bounded by the curve here:

https://brainly.com/question/27142412

A region in the plane is bounded by the graph of y=1/x, the x-axis, the line x=m and the line x=3m, m>0. the area of this region: Ais independent of m Bincreases as m increases Cdecreases as m increases Ddecreases for all m<1/3 Eincreases for all m<1/3

Verified Answer :

What is the area under the curve?

Related Questions

A region in the plane is bounded by the graph of y=1/x, the x-axis, the line x=m and the line x=3m, m>0. the area of this region:

Ais independent of m
Bincreases as m increases
Cdecreases as m increases
Ddecreases for all m<1/3
Eincreases for all m<1/3