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

Advanced functions, writ the equation that describes the motion of a point ...

writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a

Definition of a function, A function is a relation for which each of the va...

A function is a relation for which each of the value from the set the first components of the ordered pairs is related with exactly one value from the set of second components of t

Definite integration-mathematics, Definite integration It involve integ...

Definite integration It involve integration among specified limits, say a and b The integral    is a definite integral whether the limits of integration are as: a and b

Geometry, #pqrs is a parallelogram its adjacent side is 2:1.state tHE angle...

#pqrs is a parallelogram its adjacent side is 2:1.state tHE angles

Fractions, What fraction could you add to 4/7 to get a sum greater than 1

What fraction could you add to 4/7 to get a sum greater than 1

George worked from 7:00 am to 3:30 pm how much he earn, George worked from ...

George worked from 7:00 A.M. to 3:30 P.M. with a 45-minute break. If George earns $10.50 per hour and does not obtain paid for his breaks, how much will he earn? (Round to the near

Strategic , Hi need a help for marketing strategic assignment Could you ab...

Hi need a help for marketing strategic assignment Could you able to help me???

Word problem, mark got 15.00 for his birthday he now has 27.00. how much di...

mark got 15.00 for his birthday he now has 27.00. how much did he start with

Pythagorean theorem, when one side of a triangle is 15cm and the bottom of ...

when one side of a triangle is 15cm and the bottom of the triangle is 12cm what would x be rounded to the nearest tenth?

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