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

What is the least number of students needed in a class, What is the least n...

What is the least number of students needed in a class to be sure that at least 6 will receive similar grade if there are five probable grades A, B,C, D and F?  Ans: Let us re

Area related to circle, If ABCD isaa square of side 6 cm find area of shad...

If ABCD isaa square of side 6 cm find area of shaded region

How many baseball cards does peter now have, Peter purchased 14 latest base...

Peter purchased 14 latest baseball cards for his collection. This increased the size of his collection through 35%. How many baseball cards does Peter now have? First, you must

Tutor, how can i apply as tutor

how can i apply as tutor

Show that aq= 1/2 perimeter of triangle abc, A circle touches the side BC o...

A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans:    Since the length o

Simple derivatives, Simple derivatives Example   Differentiate followin...

Simple derivatives Example   Differentiate following.  (5x 3   - 7 x + 1) 5 ,[ f ( x )] 5 ,[ y ( x )] 5 Solution: Here , with the first function we're being asked to

Find no. of non negative integral solutions, Find no. of non negative integ...

Find no. of non negative integral solutions x 1 +x 2 +x 3 +4x 4 =20 Solution)  140. Break them into prime factors . Put 4 = 2^2 and every variable will have factors in 2,3,5 with

Area related to circles, railway tunnel of radius 3.5 m and angle aob =90 f...

railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel

Given x+1/x=2cosy then find x^n +1/x^n, Here we know x can only be 1 or -1...

Here we know x can only be 1 or -1. so if it is 1 ans is 2. if x is -1, for n even ans will be 2 if x is -1 and n is odd ans will ne -2. so we can see evenfor negative x also an

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