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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)
factorize the following algebraic expressions
(6x+9y) + (11x+13y)
Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8
some basics problems to work
2=42gf
compare: 643,251: 633,512: 633,893. The answer is 633,512.
Inverse Functions : In the last instance from the previous section we looked at the two functions f ( x ) = 3x - 2 and g ( x ) = x /3+ 2/3 and saw that ( f o g ) ( x )
Sharon needs to make 25 half-cup servings of soup. How many ounces of soup does she required? One cup is 8 ounces, so half a cup is 4 ounces. Multiply 25 by 4 ounces to find ou
HOW WE CAN FACTORISE 12X+7X+1
(-2x^2y4)(10xy^2)^3
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