Aim for A Covid 19 : Integration

Chapter 1 : INTEGRATION

• By Substitution
• By Part
• By Partial

Prepared by : Lim Hwee Cheng
Pensyarah Matematik
Kolej Matrikulasi Johor

Find the indefintie integral of  (sin3 xcosx)dx

Let u  sin x Transform in the u terms
du  cos x
dx  (sin3 x cos x)dx   u3du
du  cos xdx
 u4 c
4

 sin4 x  c
4

Prepared by Lim Hwee Cheng

Try YourSelf 1

Find the indefintie integral of  3 cos x dx
 sin x

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answer
in

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Prepared by Lim Hwee Cheng

Find the indefintie integral of  2x cos3x dx

Lo P e T Therefore,  2x cos3x dx  uv   vdu

2x cos3x    sin 3x   sin 3x
 3  3
2x  2dx

u  2x dv  cos3x dx

du  2 v   cos3xdx  2x sin 3x  2   cos3x   c
dx 3 3 3 
 sin 3x
du  2dx 3  2x sin 3x  2 cos3x  c
39

Prepared by Lim Hwee Cheng

Try YourSelf 2

Find the indefintie integral of  x sin 2x dx

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answer
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Find the indefintie integral of  x2  x  4 dx (x  4)(x 1)
3x

Partial Form

x  AB   x2  x  4 dx   4 4)  1 dx
(x  4)(x 1) x  4 x 1 3x 5(x  5(x 1)

 A(x 1)  B(x  4)  4 ln x  4  1 ln x 1  C
(x  4)(x 1) 55

x  A(x 1)  B(x  4)

Solve : A 4 & B1
55

Prepared by Lim Hwee Cheng

Try YourSelf 3

Find the indefintie integral of  x2  1  dx
3x 2

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answer
in

Google Classroom.

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Prepared by Lim Hwee Cheng



Try
YourSelf

1

Prepared by Lim Hwee Cheng

Try  x sin 2x dx  uv   vdu
YourSelf

2

Prepared by Lim Hwee Cheng

Try  x 2  1  dx
YourSelf 3x 2

3

Prepared by Lim Hwee Cheng