C1 – Integration Summary
 Integration is the process of finding a function from its derivative.

dy
dx
=
axn
y=
a
n1
x
n1
+ c where c is an arbitrary constant that can
only be found with further information.
 Increase the power by one and divide by new power.
 Make sure you do not forget + c in indefinite integration.
 Notation:
 ax dx =
n
a
n1
x n1 + c
 Definite integration:

 Integration is the process of finding a function from its derivative.

dy
dx
= axn  y =
b
f ( x)dx   f ( x)a  f (b)  f (a)
a
a
n1
x n1 + c where c is an arbitrary constant that can
only be found with further information.
 Increase the power by one and divide by new power.
 Make sure you do not forget + c in indefinite integration.
 Notation:
 Make sure you do not forget dx as part of the notation.
b
C1 – Integration Summary
 ax dx =
n
a
n1
x n1 + c
 Make sure you do not forget dx as part of the notation.
b
 Definite integration:
 f ( x)dx   f ( x)
b
a
 When finding a definite integral writing + c is not necessary as it will
cancel out.
 Make sure your integral goes in square brackets with the limits on the
right hand side.
 Make sure you substitute in the top number first.
 Unless stated otherwise, the larger number goes on top.
 The area of the region bounded by the curve y = f(x), the x axis and the
 When finding a definite integral writing + c is not necessary as it will
cancel out.
 Make sure your integral goes in square brackets with the limits on the
right hand side.
 Make sure you substitute in the top number first.
 Unless stated otherwise, the larger number goes on top.
 The area of the region bounded by the curve y = f(x), the x axis and the
b
lines x = a and x = b is given by
 f (b)  f (a)
a

b
f ( x)dx .
a
 If the region is below the x axis the integration will give a negative value.
The area is the positive value of the integral.
 If the region is partly above and partly below the x axis evaluate as two
separate regions then add together the separate areas.
 To find the are between two curves y = f(x) and y = g(x):
method 1) find area under each curve and subtract results
method 2) find f(x) – g(x) and integrate the result
 The limits of the integration are the x coordinates of the points where
y = f(x) meets y = g(x).
 In method 2 f(x) should be the curve on top, otherwise the result will be
the negative value of the area.
lines x = a and x = b is given by
 f ( x)dx .
a
 If the region is below the x axis the integration will give a negative value.
The area is the positive value of the integral.
 If the region is partly above and partly below the x axis evaluate as two
separate regions then add together the separate areas.
 To find the are between two curves y = f(x) and y = g(x):
method 1) find area under each curve and subtract results
method 2) find f(x) – g(x) and integrate the result
 The limits of the integration are the x coordinates of the points where
y = f(x) meets y = g(x).
 In method 2 f(x) should be the curve on top, otherwise the result will be
the negative value of the area.