Proof integral function, Mathematics

Assignment Help:

Proof of: if f(x) > g(x) for a < x < b then ab  f(x) dx > g(x).

Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Property 8 proved as above we know that,

ab f(x) - g(x) dx > 0

We know as well from Property 4,

ab f(x) - g(x) dx = ab f(x) dx - ab g(x) dx

Therefore, we then get,

ab f(x) dx - ab g(x) dx > 0

ab f(x) dx > ab g(x) dx

Proof of: If m ≤ f(x) ≤ M for a ≤ x ≤ b then m (b - a)≤ ab f(x) dx ≤ M (b - a).

 Provide m ≤ f(x) ≤ M we can utilize Property 9 on each inequality to write,

ab m dx < ab f(x) dx ≤ ab M dx

So by Property 7 on the left and right integral to find,

m(b -a) < ab f(x) dx ≤ M (b -a)


Related Discussions:- Proof integral function

Estimate percent of the original price will the customer pay, Bikes are on ...

Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price? The original price of the bike

Equal matrices - linear algebra and matrices, I need assignment help for Eq...

I need assignment help for Equal Matrices. can you please define Equal Matrices?

Ann, What was last years salary if after a 3% increase the salary is 35,020...

What was last years salary if after a 3% increase the salary is 35,020?

Find out the different strategies of multiplications, 1. Give some Class 4 ...

1. Give some Class 4 children around you problems like 15 x 6 to do dentally. Interact with them to find out the different strategies they use for doing it, and note these down.

The value of m+n, Every point (x,y) on the curve y=log2 3x is transferred t...

Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve

Unitary method, what is the history of unitary method

what is the history of unitary method

Unite Ratet, How does finding the unit rate help make smart decisions?

How does finding the unit rate help make smart decisions?

Methods of set representation, I have an assignment of set theory, please E...

I have an assignment of set theory, please Explain Methods of set representation.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd