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

Function notation, Now we need to move onto something called function notat...

Now we need to move onto something called function notation.  Function notation will be utilized heavily throughout most of remaining section and so it is important to understand i

Complementary addition model, E1) How is the 'comparison model' different...

E1) How is the 'comparison model' different from the 'complementary addition model'? E2) Create one word problem related to the children's world for each of the 4 models liste

Video games, Should video game companies continue to alter their products t...

Should video game companies continue to alter their products to include other functions, such as e-mail

Ratio, the ratio of dogs to cats is 2 to 9.if there are 10 dogs how many ca...

the ratio of dogs to cats is 2 to 9.if there are 10 dogs how many cats are there?

Word problem time vs desent, altitude 35000 @ 9:30 9;42 alt 17500 increase...

altitude 35000 @ 9:30 9;42 alt 17500 increase speed by factor of 3 level out at 2500= how much time will it take

Please solve this question, The number of integral pairs (x,y) satisfying t...

The number of integral pairs (x,y) satisfying the equation x^2=y^2+1294 is a)2 b)3 c)4 d)None of these

Math makes sense pg 261 #3 c., A seahorse layes about 200 eggs.How would yo...

A seahorse layes about 200 eggs.How would you include this data on your pictograph.would you need to change anything.Explain the change.show your work.

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