Integration
Twitter: @Owen134866
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Simplify these expressions: 3) Sketch the curves with the
following equations:
a) 𝟓
𝟐
b) 𝟑
𝒙 𝟐𝒙 𝟐
a)
c) d)
𝟓 𝟑
𝟐
𝒙 −√ 𝒙
−
𝟐 −𝟏 𝟑
2) Find when equals: 𝒙 +𝟒 𝒙
−𝟑
b)
a) b)
𝟓
c) 𝟔 𝒙d)
𝟐
+𝟑 𝒙 −𝟏
−𝟓 −𝟏
𝟏 𝟐
𝟐 − − 𝟑 𝒙
𝟑 𝒙 +𝟐 𝒙 𝒙𝟐
,Teachings for
Exercise 13A/B
, Integration
Integration is the reverse process
of differentiation.
Differentiating Integrating
Lets think about the process Function Function
forwards and backwards…
y x 2
Multiply by the Divide by the
dy power new power
2 x
dx
So integrating 2x
y x 2 5 should give us x2, but Reduce the Increase the
we will be unsure as to power by 1 power by 1
dy
2 x whether there is a
dx constant, and what it
might be…
Gradient Gradient
y x2 - 7 Function Function
dy
2 x
dx What if we had to integrate 2x?
13A/B
Twitter: @Owen134866
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Simplify these expressions: 3) Sketch the curves with the
following equations:
a) 𝟓
𝟐
b) 𝟑
𝒙 𝟐𝒙 𝟐
a)
c) d)
𝟓 𝟑
𝟐
𝒙 −√ 𝒙
−
𝟐 −𝟏 𝟑
2) Find when equals: 𝒙 +𝟒 𝒙
−𝟑
b)
a) b)
𝟓
c) 𝟔 𝒙d)
𝟐
+𝟑 𝒙 −𝟏
−𝟓 −𝟏
𝟏 𝟐
𝟐 − − 𝟑 𝒙
𝟑 𝒙 +𝟐 𝒙 𝒙𝟐
,Teachings for
Exercise 13A/B
, Integration
Integration is the reverse process
of differentiation.
Differentiating Integrating
Lets think about the process Function Function
forwards and backwards…
y x 2
Multiply by the Divide by the
dy power new power
2 x
dx
So integrating 2x
y x 2 5 should give us x2, but Reduce the Increase the
we will be unsure as to power by 1 power by 1
dy
2 x whether there is a
dx constant, and what it
might be…
Gradient Gradient
y x2 - 7 Function Function
dy
2 x
dx What if we had to integrate 2x?
13A/B
