082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Review exercises 15 479
(d) 0.7071
(e) 0.7071
√
1
(f)
2 + sinπωcosπω
2πω
(g)
√
1 + sin2 ω
ω
4 (a) 1.5811 (b) 1.3466 (c) 2.2724
REVIEWEXERCISES15
1 Find the average value ofthe following functions
acrossthe specified interval:
(a) f (t) = 3 −t across[0,4]
(b) f(t) =t 2 −2across[1,3]
(c) f(t)=t+ 1 across [1,4]
t
(d) f(t) = √ t +1 across [0,4]
(e) f (t) =t 2/3 across [0,1]
2 Calculatethe average value ofthe following:
[ ]
(a) f (t) = 2sin2t across 0, π 2
[ ]
(b) f (t) =Asin4t across
0, π 2
(c) f (t) = sint +cost across [0,π]
( ) [ ]
t
(d) f(t) =cos across 0, π 2 2
(e) f (t) = sintcost across [0, π]
3 Calculate the averagevalue ofthe following
functions:
(a) f (t) =Ae kt across [0,1]
(b) f(t) = 1
e 3t across [0,2]
(c) f (t) = 3 −e −t across [1,3]
(d) f (t) = e t +e −t across[0,2]
(e) f (t) =t +e t across[0,2]
4 Find the average andr.m.s.values of
Acost +Bsint across
(a) [0,2π]
(b) [0, π]
5 Find the r.m.s.values ofthe functions
in Question1.
6 Find the r.m.s.values ofthe functionsin
Question2.
7 Find the r.m.s.values ofthe functions
in Question3.
Solutions
1 (a) 1
7
(b)
3
(c) 2.9621
7 3
(d) (e)
3 5
4
2
2 (a) (b) 0 (c)
π
π
(d) 0.9003
(
(e) 0
)
e k −1
3 (a)A
k
(b) 0.1663
(c) 2.8410 (d) 3.6269
(e) 4.1945
4 (a) average = 0, r.m.s. =
√
A 2 +B 2
2
(b) average = 2B π ,r.m.s. = √
A 2 +B 2
5 (a) 1.5275 (b) 3.2965 (c) 3.0414
(d) 2.3805 (e) 0.6547
6 (a) 1.4142 (b)
2
A
√
2
(c) 1
(d) 0.9046 (e) 0.3536
√
e 2k −1
7 (a)A (b) 0.2887
2k
(c) 2.8423 (d) 3.9554
(e) 4.8085