13. Integration

Question 1

Indefinite Integration

Answer 1

The reverse of differentiation

1. Add one to each power
2. Divide the coefficient by the new power
3. When you have done that for each put a +c

Question 2

Integration notation

Answer 2

∫ equation d variable

e.g. ∫ 10x dx

Question 3

How to find c when given a point the curve passes through

Answer 3

Substitute x and y to see what c must be to make both sides equal

Question 4

Definite Integration Uses

Answer 4

Finding the area under a graph

Question 5

Definite integration

Answer 5

Notation the same as indefinite but with the upper limit at the top right of the ∫ and lower at the bottom right
Integrate as normal without a c and rite in square brackets and put the limits at the right of that
Substitute each limit and find the difference between

Question 6

Area between a curve, the x-axis, x = a and x = b

Answer 6

Integrate the equation of the curve definitely between x = a and x = b

Question 7

If you want the area above the x-axis but it is in two regions

Answer 7

It doesn’t matter, integrate between max and min roots still

Question 8

How to find an area under the x-axis

Answer 8

Find the area normally by integrating and then take the positive value

Question 9

When some is over and some is under the x-axis

Answer 9

Integrate separately between each neighbouring roots and sum the positive values of each

Question 10

Area above a line but below a curve

Answer 10

Integrate the curve up to the point of intersection and subtract the area under the line (don’t need to integrate for that)

Question 11

Shortcut for areas between lines and curves

Answer 11

Subtract the lower function from the higher one and take the integral of that

Question 12

If one part of a definite integral is negative

Answer 12

Keep it as negative and do the subtraction