Analysis and Approaches for IBDP Maths Ebook 2 | Page 171

51
Example
Paper 1 Section A – Integration by Substitution
12
It is given that
ln 20
2
x
� xe dx � 8. Find the value of c .
lnc
[5]
Solution
�
ln 20
lnc
xe
x
2
dx � 8
2
x
Let u� e . (M1) for substitution
du
2 1
2
x
x
2xe du xe dx
dx � � 2
�
x � � u � e �
ln20
ln 20 20
lnc
x � ln c � u � e � c
20 1
�� d u � 8
(A2) for correct working
c
2
�1
�
�
u
�
� �
2
c
20
� 8
A1
1 1
(20) 8
2 � 2 c �
20 �c
� 16
c � 4
A1
[5]
Exercise 51
1. It is given that
2. It is given that
1
4
k
4x
3 3 28
� e � d x � e ( e �1)
. Find the value of k .
0
3
0 sin x k
� dx
� �ln 2. Find the value of k .
cos x 8
�
�
3
[5]
[6]
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