Intergration

Question 1

How do you integrate?

Answer 1

Increase the power by one and divide by the new power

Question 2

How do you prepare for intergration?

Answer 2

Change roots to powers
X must not be on the denominator
Expand any pairs of brackets

Question 3

When integrating an indefinite integral (one with no limits) what must we always remember?

Answer 3

+C

Question 4

Why do we intergrate?

Answer 4

To find the area under a curve or to recover f (x) from f ‘(x)

Question 5

What do you get if you intergrate sinx?

Answer 5

• cosx + c

Question 6

What do you get if you intergrate cosx?

Answer 6

Sinx +c

Question 7

What do you get if you intergrate sin(ax+b)?

Answer 7

-1/a cos(ax+b) +c

Question 8

What do you get if you intergrate cos(ax+b)?

Answer 8

1/a sin(ax+b) +c

Question 9

What do you get if you intergrate (ax+b) to the power of n?

Answer 9

(ax + b) to the power of n+1 / a (n+1) +c

Question 10

What did we have to remember when the enclosed area is below the x-axis?

Answer 10

The answer will be negative, so we explain this fact and change the answer to positive

Question 11

What do we have to remember when the area is partly above and below the x-axis?

Answer 11

We have to work out the areas separately ( one above x-axis, one below) then add them together

Question 12

How do we find the area between two curves or a line and a curve?

Answer 12

Intergrate (curve above - cure below)

Question 13

How do we find where the curves meet?

Answer 13

y=y and solve

Question 14

What do we get if we integrate speed?

Answer 14

Distance

Question 15

What do we do if we intergrate acceleration?

Answer 15

Speed

Question 16

How do you integrate with chain rule?

Answer 16

1) integrate the bracket (ignoring what’s inside)
2) divide by the differential of what’s inside the bracket