Higher Engineering Mathematics

IRREGULAR AREAS, VOLUMES AND MEAN VALUES OF WAVEFORMS 223

C

Figure 20.13

2. Find the average value of the periodic wave-
   forms shown in Fig. 20.14 over one complete
   cycle. [(a) 2.5 V (b) 3 A]


3. An alternating current has the following val-
   ues at equal intervals of 5 ms

Time (ms) 0 5 10 15 20 25 30

Current (A) 0 0.9 2.6 4.9 5.8 3.5 0

Figure 20.14

Plot a graph of current against time and esti-

mate the area under the curve over the 30 ms

period using the mid-ordinate rule and deter-

mine its mean value.

[0.093 As, 3.1 A]

4. Determine, using an approximate method,
   the average value of a sine wave of maxi-
   mum value 50 V for (a) a half cycle and (b) a
   complete cycle. [(a) 31.83 V (b) 0]


5. An indicator diagram of a steam engine is
   12 cm long. Seven evenly spaced ordinates,
   including the end ordinates, are measured as
   follows:

5.90, 5.52, 4.22, 3.63, 3.32, 3.24, 3.16 cm

Determine the area of the diagram and the

mean pressure in the cylinder if 1 cm repre-

sents 90 kPa. [49.13 cm^2 , 368.5 kPa]