Integration

Question 1

How do you integrate?

Answer 1

Increase the power by one, then divide by the new power

Question 2

How do you prepare for integration?

Answer 2

Change any roots into powers

x must not be on the denominator of any fraction

Any brackets pairs must be expanded

Question 3

When integrating an indefinite integral, what must we always remember?

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 you get if you integrate:
Sin x ?
Cos x ?

Answer 5

-cos x + c
Sin x + c

Question 6

What do you get if you integrate:
Sin(ax + b) ?
Cos(ax + b) ?

Answer 6

-1 over acos (ax + b) + c
1 over asin (ax + b) + c

Question 7

What do you get if you integrate (ax + b)? ( = n/power)

Answer 7

(ax + b)}
a(n + 1)} + c

Question 8

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

Answer 8

The answer will be negative, so we explain this as we change it to positive (-5 does not equal 5. Eg. as the area is below the x-axis the answer is negative)

Question 9

What do we do if the area is partly above and below the x-axis?

Answer 9

Work out the sections separately then add them together

Question 10

How do we find where curves meet?

Answer 10

Use y=y and solve