Week 17 Definete integrals Flashcards
What are definete integrals?
A definite integral represents a number when the lower and upper limits are constants
F(x) is the antiderative of f(x)
Why dont we include the constant of integration?
With definite integrals, if we have a constant multiple, what do we do with it?
What is the addition and subtraction rule for definite intergrals?
Why are definte intergrals useful?
they tell us about an area under the curve
If we have a non positive integrand, meaning we get a negative area but what do we do?
We find the magnitude of the answer
How do we find the area of a hatched region?
Depending on each section we find the area of each and add together.
SO what is the procedure of finding the area of the region bounded by the curve y = f(x), the x axis and the vertical lines x = a and x=b
Be careful about the exact area, if you try to solve this definite integrand as a whole you will not get the right answers so we need to the correct sections.
How can we use integration for definite intergrals by susbutition?
1) find g and and put the limits on the integrand into g to find new limits.
2) solve it as a normal integration by subsitution question
How do we find definite integral using integration by parts?
we just solve using integration by parts, then when you get your answer, but the limits on the answer, then find the answer.
What is an economic application of definete integrals?
Finding consumer and producer surplus.
What is producer surplus and consumer surplus?
CS = the difference between price that consumers and willing to pay and the price they actually pay for good.
PS = defined as the difference between the amount the producer is willing to supply goods for and the actual amount received by him when he makes the trade.
How do we work out CS AND PS?
