STANDARD INTEGRATION 373
H
- (a)
∫ 2
1
cosec^24 tdt
(b)
∫π
2
π
4
(3 sin 2x−2 cos 3x)dx
[(a) 0.2527 (b) 2.638]
- (a)
∫ 1
0
3e^3 tdt (b)
∫ 2
− 1
2
3e^2 x
dx
[(a) 19.09 (b) 2.457]
- (a)
∫ 3
2
2
3 x
dx (b)
∫ 3
1
2 x^2 + 1
x
dx
[(a) 0.2703 (b) 9.099]
- The entropy changeS, for an ideal gas is
given by:
S=
∫T 2
T 1
Cv
dT
T
−R
∫V 2
V 1
dV
V
whereTis the thermodynamic temperature,
Vis the volume andR= 8 .314. Determine
the entropy change when a gas expands from
1 litre to 3 litres for a temperature rise from
100 K to 400 K given that:
Cv= 45 + 6 × 10 −^3 T+ 8 × 10 −^6 T^2
[55.65]
- The p.d. between boundariesaandbof an
electric field is given by:V=
∫b
a
Q
2 πrε 0 εr
dr
Ifa=10,b=20,Q= 2 × 10 −^6 coulombs,
ε 0 = 8. 85 × 10 −^12 andεr= 2 .77, show that
V=9kV.
- The average value of a complex voltage
waveform is given by:
VAV=
1
π
∫π
0
(10 sinωt+3 sin 3ωt
+2 sin 5ωt) d(ωt)
EvaluateVAVcorrect to 2 decimal places.
[7.26]
