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 vertex form for a quadratic equation, What is the Vertex Form f...

What is the Vertex Form for a Quadratic Equation ? The vertex form for a quadratic function is as follows: f(x) = a(x - h) 2 + k The graph of this function Is a parabola whos

4 accounting majors, 4 accounting majors, 2 economics majors and 3 marketin...

4 accounting majors, 2 economics majors and 3 marketing majors have an interview for5 different positions with a large company. Find the number of dfferent ways that 5 of these c

Algebra, Evaluate: 30 - 12÷3×2 =

Evaluate: 30 - 12÷3×2 =

Example of multiplication of complex numbers, Multiply following and write ...

Multiply following and write the answers in standard form.  (a) 7 i ( -5 + 2 i )  (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu

#tiword problem proportions, The scale of a map is 0.5 in 25mi the actua...

The scale of a map is 0.5 in 25mi the actual distance between two cities is 725mi write a proportion that represents the relationship how far apart will the cities be on the map

Write down the equation of the line, Write down the equation of the line wh...

Write down the equation of the line which passes through the points (2, -1, 3) and (1, 4, -3).  Write all three forms of the equation of the line. Solution To do the above

Evaluate the slope of the line, Evaluate the slope of the line: Examp...

Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution:            m = 125 -85/30-20 = 4

Coordinate geometry, find the points on y axis whose distances from the poi...

find the points on y axis whose distances from the points A(6,7) and B(4,-3) are in the ratio 1:2

Find the number of males and females in the village, The population of the ...

The population of the village is 5000.  If in a year, the number of males were to increase by 5% and that of a female by 3% annually, the population would grow to 5202 at the end o

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