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Proof of: if f(x) > g(x) for a < x < b then a∫b 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,
a∫b f(x) - g(x) dx > 0
We know as well from Property 4,
a∫b f(x) - g(x) dx = a∫b f(x) dx - a∫b g(x) dx
Therefore, we then get,
a∫b f(x) dx - a∫b g(x) dx > 0
a∫b f(x) dx > a∫b g(x) dx
Proof of: If m ≤ f(x) ≤ M for a ≤ x ≤ b then m (b - a)≤ a∫b f(x) dx ≤ M (b - a).
Provide m ≤ f(x) ≤ M we can utilize Property 9 on each inequality to write,
a∫b m dx < a∫b f(x) dx ≤ a∫b M dx
So by Property 7 on the left and right integral to find,
m(b -a) < a∫b f(x) dx ≤ M (b -a)
127.78*45
SOLVE AND GRAPH THE PARABOLA NOTE: WRITE YOUR SOLUTIONS AND COMPLETE EQUATION OF GRAPH SPOINTS EACH 1. V(0,0) (0.2) P-2 2. V(0,0) E-5,0) P=-5 3. V(4-3) F(4,-2) P=1 4. V-1,5)
i need some information on this topic for my holidays project..plz guide me what to do
how to do fraction?
3x2+5x-2
Describe the Properties of Inequalities ? Postulate In comparing two quantities, say a and b, there are exactly three possibilities. (1) a is less than b. (a b)
?x7=54
2.When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the tw
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The following (artificial) data record the length of stay (in days) spent on a psychiatric ward for 28 consecutive patients who have been sectioned under the mental health act, cla
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