Week 17 Definete integrals

Question 1

What are definete integrals?

Answer 1

A definite integral represents a number when the lower and upper limits are constants

Question 2

Answer 2

F(x) is the antiderative of f(x)

Question 3

Why dont we include the constant of integration?

Answer 3

Question 4

With definite integrals, if we have a constant multiple, what do we do with it?

Answer 4

Question 5

What is the addition and subtraction rule for definite intergrals?

Answer 5

Question 6

Answer 6

Question 7

Why are definte intergrals useful?

Answer 7

they tell us about an area under the curve

Question 8

Answer 8

Question 9

Answer 9

Question 10

If we have a non positive integrand, meaning we get a negative area but what do we do?

Answer 10

We find the magnitude of the answer

Question 11

How do we find the area of a hatched region?

Answer 11

Depending on each section we find the area of each and add together.

Question 12

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

Answer 12

Question 13

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.

Answer 13

Question 14

How can we use integration for definite intergrals by susbutition?

Answer 14

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

Question 15

Answer 15

Question 16

How do we find definite integral using integration by parts?

Answer 16

we just solve using integration by parts, then when you get your answer, but the limits on the answer, then find the answer.

Question 17

Answer 17

Question 18

What is an economic application of definete integrals?

Answer 18

Finding consumer and producer surplus.

Question 19

What is producer surplus and consumer surplus?

Answer 19

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.

Question 20

How do we work out CS AND PS?

Answer 20

Question 21

Answer 21