C4
1
Integrate with respect to x
3
b sin 4x
c cos
e cos (2x − 1)
f 3 sin ( π3 − x)
g sec x tan x
5 sec2 2x
j cosec
π
2
a
∫0
d
∫0
π
3
cos x dx
6
7
π
3
cos (2x −
) dx
∫
1
4
x
k
π
4
)
h cosec2 x
4
sin 2 x
l
1
cos 2 (4 x + 1)
π
6
b
∫0
e
∫
π
3
π
4
π
2
sin 2x dx
c
∫0
sec2 3x dx
f
∫
1
2
2 sec
2π
3
π
2
1
2
x tan
x dx
cosec x cot x dx
tan2 x dx = tan x − x + c.
a Use the identity for cos (A + B) to express cos2 A in terms of cos 2A.
∫
cos2 x dx.
Find
a
∫
sin2 x dx
b
∫
cot2 2x dx
c
∫
sin x cos x dx
d
∫
sin x
cos 2 x
dx
e
∫
4 cos2 3x dx
f
∫
(1 + sin x)2 dx
g
∫
(sec x − tan x)2 dx
h
∫
cosec 2x cot x dx
i
∫
cos4 x dx
Evaluate
π
2
a
∫0
d
∫
π
4
2 cos2 x dx
b
∫0
cos 2 x
sin 2 2 x
e
∫0
π
4
π
6
dx
π
4
cos 2x sin 2x dx
c
(1 − 2 sin x)2 dx
f
∫
π
2
π
3
tan2
∫
π
3
π
6
sec2 x cosec2 x dx
1
2
x dx
a Use the identities for sin (A + B) and sin (A − B) to show that
sin A cos B ≡
b Find
8
x cot
d sin (x +
a Express tan2 θ in terms of sec θ.
b Find
5
1
4
x
Evaluate
b Show that
4
1
2
a 2 cos x
i
2
Worksheet D
INTEGRATION
∫
1
2
[sin (A + B) + sin (A − B)].
sin 3x cos x dx.
Integrate with respect to x
a 2 sin 5x sin x
b cos 2x cos x
c 4 sin x cos 4x
 Solomon Press
d cos (x +
π
6
) sin x