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

Monomial, express the area of a square with sides of length 5ab as monomial...

express the area of a square with sides of length 5ab as monomial

Math134, how to sketch feasible set

how to sketch feasible set

Word problem, tom has 150 feet of fencing to enclose a rectangular garden. ...

tom has 150 feet of fencing to enclose a rectangular garden. if the length is to be 5 feet less than three the width, find the area of the garden

7th grade math, it cost $520 to plant 4 acres of corn. how much would it co...

it cost $520 to plant 4 acres of corn. how much would it cost to plant 3/5 acre of corn

An aeroplane is flying , An aeroplane is flying at a specific height of 5 k...

An aeroplane is flying at a specific height of 5 km, and at a velocity of 450 km/hr. A camera on the ground is pointed towards the plane, at an angle θ from the horizontal. As the

How to calculate probability of event, Q. How to calculate Probability of e...

Q. How to calculate Probability of event? Ans. What chance do I have to toss the coin and get a head? You might think 50-50, 50%. What about tossing it 5 times and getting

How high is a structure, One method of calculating the height of an object ...

One method of calculating the height of an object is to place a mirror on the ground and then position yourself so that the top of the object will be seen in the mirror. How high i

Write radicals in exponent form, Write each of the given radicals in expone...

Write each of the given radicals in exponent form. Solution As illustrated in the last two parts of this example we have to be careful with parenthesis.  While we

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

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