Basic Integration, Definite integrals and differential equations

Question 1

How to integrate

Answer 1

Increase the power by 1 the divide by new power and add c

Question 2

How to prepare for integration

Answer 2

Change any roots into powers
x must not be a denominator
Any pairs of brackets should be expanded

Question 3

When integrating an indefinite integral what must always be added

Answer 3

+c

Question 4

Why do we integrate

Answer 4

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

Question 5

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

Answer 5

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

Question 6

What must we remember when area is partly above and below the x axis

Answer 6

We have to work out the areas separately one above the x axis, one below then add together.

Question 7

How to find areas between two curves or a line and a curve

Answer 7

§(curve above eq - (curve below eq)dx
no + c
Symbol is slightly different

Question 8

How do we find when to curves meet

Answer 8

Use y=y

Question 9

What do we get if we integrate acceleration?

Answer 9

Speed

Question 10

What do we get if we integrate speed?

Answer 10

Distance