Week 15 Integration

Question 1

Explain this function which explains the basics of our integration?

Answer 1

Question 2

We are now going to integrate a constant, what is the rule for integrating constants?

Answer 2

Question 3

Answer 3

Question 4

Integrate this function

Answer 4

Question 5

What is the integration rule when x^n when n doesnt equal -1?

Answer 5

Question 6

Answer 6

Question 7

What is the integral of x^n when n = -1? when x>0

Answer 7

Question 8

How do we rewrite this?

Answer 8

Question 9

With integration what are the 2 most important components?

Answer 9

We have to include a dx and secondly we have include a constant multiple, always + c unless we have a a defined integral, which we will come to in notes 17.

Question 10

How do we integrate this function e^x?

Answer 10

Question 11

What is the constant mutiple rule for integration?

Answer 11

Question 12

Answer 12

Question 13

Verify this by using differentation

Answer 13

Question 14

Answer 14

Question 15

What the addition and subtraction rules for integration?

Answer 15

Question 16

Integrate this function and verify by differentating?

Answer 16

Question 17

We are now going look at functions of powers of simple functions of x? what 2 cases will we look at?

Answer 17

Question 18

What is the integral for this function

Answer 18

Question 19

What is the integral of the function (x+k)^n when n = -1?

Answer 19

Question 20

Answer 20

Question 21

What is the integral of (ax+b)^n?

Answer 21

Question 22

Whats the integral of (ax+b) when n = -1 and a doesnt equal 0?

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

Answer 25

Question 26

If we are given marginal cost, how do we find the cost function?

Answer 26

Question 27

Now lets look at an economic application, so we know that the anitderative of the marginal cost function is the cost function, but what is the problem?

Answer 27

We are left with an arbitary constant c, which we cannot have, so we must have information about the fixed costs ie when q =0 and given a particular value of the fixed costs, in order to find our cost function.

Question 28

Answer 28

Question 29

Answer 29

Question 30

Answer 30

Question 31

Answer 31

Question 32

Answer 32

Question 33

Answer 33

Question 34

Answer 34

Question 35

Answer 35

Question 36

Answer 36

c(30) = 10200