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

Find the quotient and remainder, Question: Find the quotient and remain...

Question: Find the quotient and remainder when f(x) = x 5 - x 4 - 4x 3 + 2x + 3 is divided by g(x) = x-2. Make sure the quotient and remainder are clearly identified.

Geometry, RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS...

RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS, ST, AND RT

Credit and invoice, mr ouma bought two sets of spanners for sh 300per set ...

mr ouma bought two sets of spanners for sh 300per set two machanic vice at sh 1000each three set of screw driver at sh 115 per set and tool box for sh 300

Matrix, cramers rule introduction

cramers rule introduction

Round 14.851 to the nearest tenth, Round 14.851 to the nearest tenth? T...

Round 14.851 to the nearest tenth? The tenths place is the ?rst number to the right of the decimal. Here the number 8 is in the tenths place. To decide whether to round up or

Partial differential equations, I need expert who can solve 10 set of PDE w...

I need expert who can solve 10 set of PDE with constant of integration.

Find the perimeter of the rectangle, Find the perimeter of the figure, wher...

Find the perimeter of the figure, where AED is a semi-circle and ABCD is a rectangle.    (Ans : 76cm) Ans:    Perimeter of the fig = 20 + 14 + 20 + length of the arc (AED

How do children learn maths?, HOW DO CHILDREN LEARN? : Have you ever tried...

HOW DO CHILDREN LEARN? : Have you ever tried teaching a young child what "ball" means? Did you do it by a lot of verbal description" Or did you let the child actually handle a b

Geometry, find the value of 0 that makes cos 21 degrees = sin 0 statement t...

find the value of 0 that makes cos 21 degrees = sin 0 statement true.

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