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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)
Determine the differential for following. y = t 3 - 4t 2 + 7t Solution Before working any of these we have to first discuss just
The equation -2x^2-kx-2=0 has two different real soultions. find the set of possible values for k.
sir/madam, i abdulla working as a maths teacher want to join ur esteemed organisation as a tutor how can i proceed i have created an account even pls guide me, thanks abdulla
For this point we've only looked as solving particular differential equations. Though, many "real life" situations are governed through a system of differential equations. See the
What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at the point (4, f(4))
1
how do i multiply and divide fractions?
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
1+2+3+78+980
2.5 in\ \/
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