418 Higher Engineering Mathematics
4.
dθ
3 − 4 sinθ
⎡
⎢
⎣
1
√
7
ln
⎧
⎪ ⎨
⎪ ⎩
3 tan
θ
2
− 4 −
√
7
3 tan
θ
2
− 4 +
√
7
⎫
⎪ ⎬
⎪ ⎭
+ c
⎤
⎥
⎦
5. Show that
dt
1 + 3 cost
=
1
2
√
2
ln
⎧
⎪ ⎨
⎪ ⎩
√
2 + tan
t
2
√
2 − tan
t
2
⎫
⎪ ⎬
⎪ ⎭
+ c.
6. Show that
π/3
0
3 dθ
cos θ
= 3.95, correct to 3
significant figures.
7. Show that
π/2
0
dθ
2 + cos θ
=
π
3
√
3
.