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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)
what is rotation
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a company''s advertising expenditures average $5,000 per month. Current sales are $29,000 and the saturation sales level is estimated at $42,000. The sales-response constant is $2,
find h in the parallelogram
Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f
Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is
Ratio of successes in 5 independent trials to the probability of successes in two independent trials is 1/4. What is the probability of 4 successes in 6 independent trials?
can you hepl me with my home i dont understand it!!!
Suppose research on three major cell phones companies revealed the following transition matrix for the probability that a person with one cell phone carrier switches to another.
zeroes of polynomial 2x2-3x-2
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